Fundamentals of Engineering Thermodynamics | Dániel Csíkos | Skillshare

Fundamentals of Engineering Thermodynamics

Dániel Csíkos, Mechanical engineer

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52 Lessons (5h 8m)
    • 1. Introduction

      2:05
    • 2. Thermodynamical modelling

      5:52
    • 3. State variables

      3:53
    • 4. Gibbs' phase rule

      2:50
    • 5. Laws of thermodynamics

      1:55
    • 6. 0th law of thermodynamics

      4:23
    • 7. Internal energy, enthalpy

      4:05
    • 8. Work, heat

      7:15
    • 9. Work – Sample problem

      3:17
    • 10. Heat – Sample problem

      4:43
    • 11. 1st law of thermodynamics

      3:01
    • 12. 1st law of thermodynamics - Sample problem 1

      3:55
    • 13. 1st law of thermodynamics - Sample problem 2

      4:42
    • 14. 2nd law of thermodynamics - Entropy

      4:51
    • 15. 3rd law of thermodynamics

      2:13
    • 16. Fun fact - Negative absolute temperature

      3:25
    • 17. Ideal gas model

      4:03
    • 18. Relations in the ideal gas model

      5:21
    • 19. Definitions of special state changes

      6:50
    • 20. Properties of special state changes

      2:52
    • 21. Graphical representation of processes

      4:20
    • 22. Piston – Sample problem 1

      10:34
    • 23. Piston – Sample problem 2

      11:51
    • 24. Complex process - Sample problem

      9:11
    • 25. Polytropic state change – Sample problem

      8:30
    • 26. Efficiency

      5:05
    • 27. Turbine – Sample problem 1

      7:04
    • 28. Turbine – Sample problem 2

      8:18
    • 29. Compressor – Sample problem 1

      6:07
    • 30. Compressor – Sample problem 2

      8:09
    • 31. Multi stage compressor – Sample problem

      13:48
    • 32. Carnot cycle

      4:42
    • 33. Equivalent Carnot cycle

      3:41
    • 34. Equivalent Carnot cycle – Sample problem

      3:16
    • 35. Otto cycle

      7:40
    • 36. Otto cycle – Sample problem

      7:05
    • 37. Atkinson cycle – Sample problem

      6:24
    • 38. Diesel cycle

      7:21
    • 39. Diesel cycle – Sample problem

      8:09
    • 40. Sabathé mixed cycle – Sample problem

      6:39
    • 41. Brayton (Joule) cycle

      7:10
    • 42. Brayton (Joule) cycle – Sample problem

      8:07
    • 43. Multiphase systems

      9:31
    • 44. Two phase medium – Sample problem

      4:06
    • 45. Phase diagrams of water

      4:27
    • 46. State changes of water - Sample problem

      10:52
    • 47. Rankine (Clausius) steam cycle

      6:30
    • 48. Rankine (Clausius) steam cycle – Sample problem

      8:32
    • 49. Improvement of efficiency

      4:17
    • 50. Refrigerator, heat pump

      6:55
    • 51. Coefficient of performance – Sample problem

      3:54
    • 52. Refrigerator - Sample problem

      4:10

About This Class

This thermodynamics course has mainly been created for students currently learning thermodynamics or related subjects at college/university.

Objective of the Course

The main objective of the course is to help you be able to solve thermodynamical problems. You are going to be able to calculate the occuring works, heats, energies, enthalpies, entropies or the state variables even in case of complex gas or steam cycles!

By completing this course, you are going to understand how important machines like internal combustion engines, refrigerators, etc. work.

What will I learn?

  • Basic principles of thermodynamics
  • How to calculate work, heat, internal energy, enthalpy, entropy, etc.
  • How to use the laws of thermodynamics
  • Special state changes
  • Analyzing complex processes
  • Most important gas cycles
  • Analyzing gas cycles
  • Properties of phase changes
  • How to deal with multiphase systems
  • Most important steam cycles
  • Analyzing steam cycles

What do I need to know to start the course?

You don't need any specific prior thermodynamical knowledge. The course starts from scratch and take you through the topics with detailed explanations and examples.

Some basic mathematical background is needed. The most advanced topic is integration (but it is only used several problems). You can understand most of the topics with high-school level math background.

How to make the most of this course?

There are several practice problems that you can solve by yourself. I suggest solving those problems after watching the lectures of each topic!

Transcripts

1. Introduction: Hi, there I am, Daniel Tree Kush. I have recently finished my studies as a mechanical engineer, and I would like to share my knowledge of thermodynamics so you would also have no trouble with this topic, either at the university or value are working in the industry. I have the experience of sharing my expert ties with the next generation of engineers So you can trust me that I happy to succeed in the scores. We go to every topic that relates to the technical part of time of dynamics. First of four, I introduced you to the laws of thermodynamics, which are the foundation off the hot topic. Meanwhile, you are going to learn or to use the basic notions both in terror tactical and practical sense. After you have acquired the necessary knowledge, you can learn about processes. First. I we're happy to understand how eat simple process works. Then you can move on to deal with guest cycles, which are complex processes. The guest cycles are used in engineering practice in various ways, so you can already make use of this knowledge in the industry. Finally, you can take the last step and learn how to deal of its steam cycles, in which you have to calculate with not only one but with two phrases at the time. By the end of the course, you are going to have a confident knowledge off thermodynamics, and you are going to have established starting point for your further studies in related topics. I designed this course for engineers as the technical aspect off thermodynamics are introduced. But anyone can understand the basic ideas off Tama Dynamics based on the scores. I'm looking forward to help you. So sign up for my course if you are not yet convinced than please take a look at the course description on the curriculum to make sure that these scores is developed for you. See you in the first lecture. 2. Thermodynamical modelling: before anything else. Let me tell you about some basic notations which are used in time. Madonna Mika, modeling the field of Tama Dynamics, is about the investigation off the energy transfer and describes the processes off energy compassion. This investigation is general, so it doesn't state much about the specific process, but the results can be used generally. The mother contents. Three main parts. First, there is a time of dynamic system that we would like to exert mind. This time, a dynamic system can interact with its surroundings. There are several interactions, for example, mechanical or terminal interaction. The interactions can happen to a boundary, or this boundary can profound the interaction. It is averted to summarize how the boundary can behave. The boundary can be riel or imaginary. For example, tank re percents, riel, vole. The imaginary boundary can be defined anywhere. As you wish. The Bonder determines what kind of interactions can or cannot happen between the time of dynamic system on the surroundings. One of the interactions is the material flow. If the material flow is blocked, then the system is closed. This is the case off a pistol. If there can be material flow than the system is open. This is the case, often internal combustion engine. The close system has an impermeable full in case of an open system. We can have parable or semi palm above all the semi pama before only alos the flow off specific Matt areas. But it prevents other materials from cursing the boundary. Even the improbable for doesn't mean that every interaction is plugged. There are several interactions that happen through an empire marble for so there are several more options fixed on the firm above us can be defined related to mechanical interactions. The fixed waas does not alone mechanical interactions and obviously the deform above was load them The idea. Term of wall blocks the time on interaction by the D. A term of lose thermal interaction that can be other type of interactions for which war types can be defined. But these are the most important cases. Generally, we can see that an isolating fall disables all interactions between the time a dynamic system on the surroundings. Also, the idea. Batic ball is important as it only alos mechanical interactions on blocks. Everything else So we have that with the boundaries. I do not really go into details about the surroundings, but you still have to know more about the time with dynamic system, as it is a very important part of the model. Now let me show you the main aspect, and you can learn about the details in the upcoming lectures. First of all, it is very important to note the thermodynamics used macroscopic description. There are lots of microscopic processes like the movement and collision off the particles. The channel be examined in detail to solve given engineering task to describe the state off a system, it is enough to use a macroscopic quantity like a temperature or pressure. Some quantities are cored state for reliables. These state variables are unique functions off the state of the system, so they are independent from the time history and the previous processes. Not all of the quantities qualify for this creek area. So not over. I arbors are state where I, a bus, the state Mariah Berbers are not independent of each other, but they are connected through the recreations off state. One of these recreations is the Valle known idea. Gas slow material properties are also important. If you want to describe the time a dynamic system as they also appear in the creations. For example, the specifications is a material property that you need to use a lot. Finally, I have to mention faces and component. First, I am going to show you systems with one phrase and fun component. But it is very important to learn how to deal with to face systems like the steam cycle, which includes both steam on voter. It is important to see that there are not only solid liquid and gas faces, but there are ella tropes. For example, graphite and diamond are to Allah troops off carbon. They are considered as two different faces because their properties differ. We consider material with identical properties to be involved phase. But obviously graphite and diamond are not behaving the same, so they must be treated separately. Multi component systems are not mentioned a lot of times, but in fact we use them almost all the time as air is also multi component system as it contains nitrogen, oxygen and other molecules. However, when we calculated air, we don't care about components, but we treated as a whole because engineers are lazy and this method works well 3. State variables: state where I arbors described the thermodynamic system, so you always need to use them in time a dynamics as it has been stated in the previous lecture. The state variables are macroscopic properties of the system, which are unique, so they are independent of time. They only depend on the current state of the system. First off, well, classifying off state Arribas is important. One class is the class off extensive state Arribas. These are additive quantities that are proportional to the size of the system. If the time a dynamic system is divided in two parts and the extensive state for I arbors off the parts are some, they result in the value off the state. For I about that describes the whole system. Mass volume and internal energy are such state reliables. The other class belongs to the intensive state where I Arbour's. These are known additive quantities. They are the properties off a given point. If the Tama dynamic system is an actual Librium and it is divided in two parts, the value off the intensive state variables is the same in every part. If the value is not the same every for inside the system there's in homogeneity in her majority causes the flow off extensive quantities to reach eh, quality off the intensive quantities. You will understand this with an example. If the pressure is not the same every fair, then there will be material flow. You can experience it if you go outside and feel the wind temperature and pressure at the two most commonly used intensive state variables. Sometimes we use alternative forms of the state where I a bulls because they fit better to the given technical problem, one form means the specific state varietals. Specifics state for eyeballs are formed by dividing an extensive quantity with an other extensive quantity. The result is no longer extensive. It doesn't describe the size of the system anymore. They are important in case of open systems like in case of internal combustion engines or gas turbines. But the materia goes through the system. In such cases, it doesn't really matter how much the volume or the weight of the material is. The specific quantities are important. The most important case in practices. One. We take the specific state for eyeballs with respect to the mass. This is clearly indicated in the notations to capital V belongs to the volume and small we belongs to the specific volume and analogous lee or specific quantities which were made by dividing with the mass are marked with small letters may invite. All extensive quantities are marked with capital letters. The other alternative form is the flow rate off the state. For eyeballs to introduce them, it is necessary to know the definition off the mass flow rate. It is the total differential off mass with respect to time. So basically the change of the mass during unit time change the mass flow rate, perhaps to construct other rates. For example, the volume flow rate. The volume flow rate equals to the product off the mass flow rate and the specific volume. You can easily see that this means the change of the volume during unit time. All other rates are defined analogous Lee as the product off the mass flow rate on the specific quantities 4. Gibbs' phase rule: gives face rule is a very important creation from which you can deduct harmony state for IAB us to use to sufficient to describe the time a dynamic system the recreation reads as AF plus B equals two C plus two. Here, f is the number of degrees of freedom. It means the number of intensive state for I, others that can be choosing independently of each other in the given system. P is the number of phases see is the number of components. The two means that only mechanical and thermal interaction can happen. In addition to the chemical interactions off each component in the generally creation, there is small and on the right hand side, which means the number of interactions in the present case, the number of interactions, even to the number of components plus two. Because of the mechanical and thermal interactions, therefore gives face low is a special case, but usually this case is used in time of dynamics. Let's concentrate on practical use of the low. Very often we have to investigate systems with one face on van component. In that case, P and CR equal to one, which means that the number of degrees of freedom is to therefore to intensive state for I . Abbas described the system, for example, temperature and pressure in case of to face systems with fun component, such as if there is a mixture of voter and steam, there is only one degree of freedom. According to this, only one intensive state friable, is enough to describe the system. For example, the temperature. Therefore, the pressure is the function of the temperature, such as every other intensive state. Variable is the function off the temperature. If the number off phases increases to three, such that P equals to tree and Sequels to one than the number of degrees of freedom equals 20 This can sound weird for the first time, but there is actually a state in which the intensive state where I Obus doesn't change and you can see three phrase off one compliment. This is only one point on the diagrams, and it is called three per point. For example, in case off water, the tree per point can be reached at low pressure around zero degrees sauces In the Trooper Point, there is ice, voter and steam. At the same time, 5. Laws of thermodynamics: in the upcoming lectures, you can learn about the loaves off thermodynamics. Let me share some thoughts about them in advance by the loves of time of dynamics. We mean four loaves that are numbered from zero to third. The loves of thermodynamics are empirical loves. That's why I put loves between apus troves with precise use of terminology. We should say that these are rather the axioms off dammit dynamics, as they cannot be proven. They cannot be deducted mathematically either from each other or from Oliveras. These lows are purely based on experiments and observation, so the phrasing off the lows changed time to time. It cannot be stated that one phrasing is better than another, so multiple phrasing is present in the literature. Because of this, you might have seen different phrasings, and not even that I use in the upcoming lectures. But it does not mean that either my use off birds or the other one is wrong. The phrasing is different, but the essence off the low remains the same. You might think that you don't really need theory. You just want to solve engineering problems. But there is significance off these lows in practice Technik ER calculations are partly based on these loaves. For example, the first low is frequently used in analysing the processes. Also, a significant result is that the lows made it possible to define temperature, which is the intensive state reliable off the thermal interaction. It is useful to know the laws of thermodynamics, but you do not have to know them by heart. Just please concentrate on the meaning off each low. 6. 0th law of thermodynamics: Let's start discussing the lows of Tama Dynamics by the zeroth low. Let me read you zero clo involved Phrasing If two systems which can interact are actually Librium than they have exactly Azman intensive state where I a burst with identical value in the two systems as many interactions that common vaal alos What does this mean? There are two systems they are actually bring by themselves. They are actually beom with each other if they are actually Librium. Considering every possible interaction, every interaction has a characteristic intensive state. Friable, for example. Temperature belongs to the turmoil interaction. The systems can only be in time. Electra Librium. If the temperature is the same in them, you can think about every other interaction in this way. Basically, this low introduced the temperature as an intensive state reliable that helps to describe actually bloom in means off a Saturn interaction. Let's talk a bit about the actual Librium, as it appeared in the zero clo in a system in its own state off Internet timer dynamic actual Librium. No macroscopic change occurs then the intensive state where I arbors have homogeneous distribution within the system. So the intensive state reliables have the same value in every point within the system or so as it has already been stated. At the time of dynamic modeling, only the macroscopic state is in interest on micro scale. There is no actual Librium. So the macroscopic actually bloom is a dynamic equilibrium. The Tama dynamic equilibrium is symmetric. So if system A is an actual Libyan with system be System B is also in actual Librium with system A. Also, the actual Librium is transitive. So if system A is an actual Librium with system be on system be is in actual Librium with system see than A and C are also in actual ably. Um, this is an obvious consequence as the equity off all intensive state where I ambers are required for actual Librium. The actually William ST is uniquely described by the help off the intensive state. For I abuzz, you might think about one or two country examples like the supercooled liquid, a super could liquid is in liquid face even though its temperature is below freezing point at the given pressure, so had given temperature pressure on other state where I of us that can be voter and ice which seems to be controversy ary. The solution is simple. The super could liquid is not in stable but in matter stable state. So it is not exactly in its actual Librium state. If there's a proper exhortation, the liquid with instantly freeze and take it stable, solid, actually broom state. So the uniqueness off thermodynamic. Actually, Librium is only through for stable. Actually, broom states there is one but only one well defined. Actually, Priem it is voted to mention the Lucia Terry Brown principle. If the actually boom off a system in stable. Actually, Librium state is disturbed that such thermodynamic processes occur that try to reduce or eliminate the disturbance. This basically means that the system tries to evade the disturbance. It is enough if you just remember this short consequence. If I want to summarize briefly, I can say that you must remember that the zero to love Tom Madonna mix is related to the thermodynamic. Actually, Librium and the introduction off the temperature 7. Internal energy, enthalpy: moose, Internal energy and an toppy are important state for ironbirds off the term a dynamic system and they are included in the first law of thermodynamics. So you must be family or with them. Let's start with internal energy. It is the sum off several energy types with their with macroscopic processes, but in the background there are microscopic processes to their energies are included in the term internal energy. So the internal energy contents the kinetic energy off molecules which can be stored in the motion rotation or vibration off molecules. The internal energy also contains potential energy. It can be the electric potential between the molecules as they attract and refuse each other. Or so there is the potential energy off atoms. As the components off atoms are interacting with each other, it is very advantages to use the Internet energy as we can forget about the details of these micro scale effects, the internal energy is denoted by capital you as usual, the specifically entity is denoted by small you and it is called specific internal energy. The internal energy is divided by the mass. To get the specific internal energy, it can be proven that the internal energy is a state for reliable. In practice, this means that it can be calculated as a unique function off the other state for Arribas. Therefore, it doesn't matter how a process happens on Lee. The state fireballs at the two endpoints are needed to calculate the change off internal energy. This is not true for work or heat, so it is a clear advantage off internal energy. The internal energy is an extensive state for reliable. Naturally, the energies are added. If we calculate with the resultant off two sets of material zero point off the Internet, energy can be choosing arbitrary as it is not connected to any physical phenomenon. This is not a huge problem, as we usually calculate, with the change of the internal energy in case of a given time, a dynamic system, the total energy is the some off the kinetic potential and Internet energies. The kinetic and potential part relates to the properties off the resultant off the system. So there is a kinetic energy if there is a dedicated direction off mass flow. But random motion off molecules are already included in the internal energy. In technical problems, you can usually need, like the kinetic and potential energy, so you can calculate with the internal energy instead of using the total energy. The entropy is similar to the internal energy, and it is also a very important quantity. You can use the internal energy to characterize close systems while until be characterizes open systems to or from which there can be material transport with the material transport or so there is energy transport. The description off this additional energy change is easy by the half off the Antara p The entropy is denoted by capital age on the specific inter P is denoted by small age. By definition, the in therapy is originated from the Internet energy and the internal energy, plus the product off pressure and volume equals to go into a P, or we can calculate the same with the specific quantities. Inter P is an extensive state friable, which is a clear consequence off its definition. The total inter P can be defined analogous Lee to the total energy. The only differences that the anti P shall be added to the kinetic and potential energy instead of the Internet energy 8. Work, heat: before introducing the first law of thermodynamics. It is necessary to be family over the definition off the two types of work on the heat. First, let's discuss the external work. It is also simply court work or pressure volume work. The external work term is more understandable after the shaft work is also introduced. The work is an energy transport quantity. There is work if there is an intensive Param Eter that is in homogeneous inside the system . In this case, the system tries to reach the homogeneous perimeter distribution through the flow off extensive quantities in everyday language. Pressure difference leads the volume change or chemical potential difference leads to material flow. In this manner, every intensive perimeter can be connected to work except the temperature temperature will be connected to heat. The infinite, as in my work, is the product often intensive quantity and the change off the extensive quantity which relates to the intensive quantity. For example, the pressure time, volume change or forced times. This place month is on the right outside. You can see this in differential form in the example, but if you want to calculate the whole process, there is an integral In the definition, the minus side ensures that the work is positive if it increases the internal energy, so the internal energy increases for positive work on decreases for negative work. With this definition, if you take a look at the graph, you can see that the area under the curve equals to the work. The work is not a state varietal. It rather characterizes the energy, transport and the change off the state of the system. As work is not a state viable, it is past dependent. The shaft work is as important, if not more important, than external work. But what is the difference? Most importantly, the external work has been defined for closed systems by the shaft. Work is used for open systems, so if there is no material flow between the system and the surroundings, the external work must be used. But if there is material flow, the Shafter must be used. The external work has already been defined by an integral andan area. On the PV graph. The calculation off the shaft work is a bit different. Not the same area is calculated on the graph. In reality, the material flow introduces edition of work during in flu, but some berk is sub Strack did during out flow. These are called flow work. On the top of these, there's external work on the system in vile. The resultant off these three works is the shaft work. I do not show you how it can be deducted, but it can be seen that the result is the area Martin. The graph in the Intergraph formula, the roll off the pressure and volume changes as the curve is projected to the other access . Also, there is no negative sign as this formula ensures that positive shaft work increases the internal energy of the system. Last but not least, let's introduce the heat. The heat is an energy transport quantity, just like the work it is in used by the homogeneity off the temperature. It is denoted by Q so far, we cannot give such definition as we have done it. In case off work. We know that he is induced by the temperature in homogeneity, but we do not know the extensive quantity related to the temperature. This extensive quantity will be the entropy, which is an abstract notion that I will explain to you later the heat is defined to be positive if it increased that internal energy and it is negative if it is decreasing, the internal energy reverted to know that the heat is past dependent just like work. You must know the whole process to calculate heat. The endpoints are just not enough. If you want the formula for the heat, you can get one by the help of the specific it the specific. It is generally denoted by small C capital. C denotes the heat capacity, but let's just concentrate on specific heat as we use it more. It is the specific quantity off the heat capacity. C. P denotes the specific Keith related to is a Barrick Processes on DSI V is the specifications off is a correct processes. The process is is a brick. If there is constant pressure and it is is a correct. If there is constant volume in case often is a barrack process, the heat can be calculated according to the integral formula. The specific it is the function of temperature, but it can be determined by experiments so you can calculate with it as an alternative solution. The average specific heat can be used which is denoted by C P over bar. The formula is similar for is a quick processes. The is a correct specific. It is used instead of the is a barrack fun. It is important to note that these formally only valid for is a brick and is a quick processes. Other vice, The specific heat and temperature is not enough to this crap. Heat is every process perimeter. The heat can be described by two states where I Arbour's. I share the next oats just for the sake off, widening your knowledge he were probably never used latent heat in the upcoming form. The infinite eczema heat can be written as seen. I used that instead of the to be mathematically correct, but it doesn't really matter for you now. The important thing is that the temperature t on the other state Viable X describes the infinite Azima heat. If I choose pressure to be X than the result is the same as before in case off constant pressure because the second term become zero as the change of pressure is zero. If the pressure is constant, Layton Treat is the perimeter marked with capital L. It can be calculated as the pressure differential off the heat with respect to perimeter acts at constant temperature in practice, the latent heat is responsible for internal energy. Change by the temperature is constant. It is just a interesting addition. Just remember that this can happen. 9. Work – Sample problem: after the definitions. Let's see a sample problem to practice. The problem is the following. A medium is compressed in a close space by a piston from volume we 12 volume V two. During the process, the pressure can be calculated based on the volume SP equals to eight times we plus b calculate the extent of work done on the system. We must calculate external work As we have a closed system. We are calculating with these data, Rayvon equals 0.4 cubic meters. V two equals 20.1 cubic meter perimeter a equals to tend bar per cubic meters or in S I units 10 to the power of six pasqua per cubic meter. Perimeter B equals to five bar or five times 10 to the power of five bus girls. The work can be calculated based on the definition off the external work in the given closed space, this means an integral formula where the pressure as the function of the volume is integrated between the end point minus one times the integral equals to the work as that's how the work becomes positive. If it increases the internal energy, we can substitute the function for the pressure. This pollen, um, is easily integrated, the integration limits can be substituted and we get the result. As the problem contained a compression, we put work into the system to increase its internal energy. The result is also positive, which fits or expectations off course. The work can be calculated graphical it too. To do that, it is necessary to obtain the pressure at the end point to calculate the one we must substitute. We want to the formula which leads to tend to the power of five Pascal's. Similarly, P two becomes four times 10 to the power of five Paschal's. The external work equals to the area off trapezoid on the PV graph. As it can be seen, the area can be calculated in multiple ways. I ever ridged the pressure on Good that p vom please p 2/2 times v tu minus. We want equal to the area. Don't forget the negative sign because it is needed for the pro Paris Off off course. We can just determine whether the work is positive or negative, and we could add this sign at the end. But it is certainly included in the definition. If the volume decreases and the pressure increases, the work is positive. This is compression. If the volume increases on, the pressure decreases. The work is negative. This means expansion. In practice, you can barely use the diner calculation off the work as the graph is not so nice, but it is verse it to know how to calculate. 10. Heat – Sample problem: Let's see of Samper problem for calculating the heat by the half off specific heat. In this problem, we put ice with an ice mass and T ice temperature on voter with anvil term US and T voter temperature to a container. We must determine the amount and properties off water and ice at the actually bloom state all necessary specific IDs on the specific latent heat off matting at given. Also, we know that the matting point is zero degrees, as is the data. Other following the ice properties are M ice equal to one kilogram and t eyes equal to minus 10 degrees. SAS is for voter on voter. Istvan Kilogram and T voter is 25 degrees c. Azeez. The specific it off ice is to kill usual over kilogram Cavin. The specific heat for voter is four point to kill a jewel over kilogram cabin. The specific latent heat off matting is 335 killer jewel over kilogram. First of all, let's think about the physical processes that appear. There's ice, which warms up on voter that cools down in the first step. We can check how much heat is required for getting into matting point for both media to form the ice up to zero degrees SAS IDs. We can calculate the heat by the previously learned formula. The product of the specific heat mass and temperature change off ice is taken. The temperature change is always the difference between the ant temperature on the starting temperature, such that the starting temperature is so abstracted from the and temperature the ice needs Vanik ILO Chua heat To reach the matting point, we can calculate in the same manner in case off water the specific heat, the mass and temperature change off water is multiplied. The result is minus 105 kilo shoe. The result is negative as this heat is given from the water to the environment and not in the other very around. If the heat goes into the voter than the results will be positive. As the cooling off voter requires more heat than how much necessary to warm the ice up, the ice definitely starts matting. Maybe all off it mouths and even gets warmer. Or maybe just some portion of the ice melts. The heat coming from matting can be calculated as the product off the specific latent heat off matting and the mass of the matted eyes. So far, we do not know how much I smarts. Let's see how much ice needs to be matted to. Could the voter down to zero degree sauces? We can rearrange the formula. The mask off matted eyes equals to the cogent off the heat and the latent heat. The voter has already could, down to some degree, as until the ice form up. So the respective portion off the heat shabby substructure did. The remaining part shall be covered by mapping the eyes. I use absolute values, so I do not have to carry the signs. The voter gives heat to the eyes, and we saw Barsa. So between their heat there is a multiplier off minus one. The result becomes zero point 254,000 kilogram, so that much ice mounts. Now we know that there is 1.254 kilogram voter at zero degrees sauces on 0.746 kilogram eyes. At zero degrees sauces, there is a case that we haven't covered. If we had needed more than bang kilogram ice to, could the voter down the amount available would not have been enough. In that case, all of the ice melts and there would be two kilograms off water. The temperature off this water could be calculated by using the recreation for the heat necessary to warn this water up as it comes from the remaining heat. 11. 1st law of thermodynamics: as you ordered in the unnecessary quantities, I can introduce you to the first law of thermodynamics. First, let's see the law of Conservation of Energy as the first low is the consequence off this low energy can neither be created nor destroyed. It can only transform from one form to another by using this low on other Africa results. The first law of thermodynamics can be introduced in several forms. The total energy often isolated system is constant. The change off internal energy off a system which interacts with the surroundings is equal to the amount of heat supply to the system, plus the amount of work done by the surroundings on the system. You can use this low in means of several formulas in case off a closed system. The change off the internal energy that are you equals to the some off the heat Q. And the work w This is the most common form off the first law of thermodynamics. But if we cannot need like the change off kinetic and potential energy, we must use a more general form. The change off the total energy equals to the heat supply to the system and the work done on the system by the environment. In this way, the change of kinetic and potential energy is taken into account beside the change off internal energy. In case of closed systems, we could steal Forget the effect off material flow as there isn't any off it. However, a lot of engineering applications, like internal combustion engines, are open systems, but there is a material flow in case of open systems. The first law of thermodynamics contains the change off anti P instead off the change off internal energy on the left hand side. Also, the shaft work is used instead of the external work as that must be used in case of open systems. More generally, the change off the total and therapy shall be written on the left hand side. You must always use the proper formula. In a given case, you must decide veteran work with an open or closed system and then you must decide whether you can make like the change of kinetic and potential energy. A clear concept prints off The first law of thermodynamics is the impossibility off the perpetual motion machines off the first kind. There is no periodical functioning machine or cycle that can do work without the use of energy, so you can only make a cycle. Do work if you supply heat into the cycle, or you can only get heat out off a cycle if you supply work into it. 12. 1st law of thermodynamics - Sample problem 1: I'm going to show you a couple of examples off using the first low off dama dynamics. Let's see the first problem w don't bear for months is transmitted for toe time to a medium in a container. The mass off the medium is, um on. The specific heat is C. The absolute value off the heat is now. This hate is transmitted from the medium to the surroundings during the heating process. As the insulation off the container is not perfect, they must determine the temperature change of the medium between the beginning and the end of the process. We know the values off the previously mentioned varietals. The mass is tang kilograms. The specific heat is 4.18 unusual over kilogram cabin. The duration off the process is 500 seconds. The performance is tree kill that, and finally the total heat transmitted from the medium to the surroundings. It's 200 kilo shoes. We are going to use the first low off Dharma Dynamics, but the basic properties off the process shabby, identified. First, we need to decide whether the system is an open system or a closed system. The equation is a big different for those two cases. Now we have a closed system as the process takes place in a container and there isn't any material flow in case often open system. Some meth area would go into the container or would go out of the container. We can stick to a close system and use the proper form off the first load off Dama Dynamics for closed systems. The change off the Internet energy equals to the some off the heat absorbed by the system and the work done on the system. What do we know? The internal energy is not known, but we do know that it can be expressed by the half off. The temperature change or task is to determine the temperature change, so we must make that appear on the right hand side. We know both terms. As the problem descriptions says to absolute value. Heat is transmitted from the medium to the surroundings. As the medium loses energy. In this process, the sign off their heat is going to be negative. On the other hand, the work is positive as a given performance is transmitted to the medium. The work equals to the product off the powerful months and the time. So the Internet energy is the product off, the specifically the mass and the temperature change. The heat is negative as the system gives it to the surroundings. The birth is positive as it is given to the system and it equals two w that time style. The only AL known is the temperature change we can re firm later. Immigration. Take care when you substitute the values. Now I use kill a jewel and kill a vat as dimensions off the specific. It is killer shoes over kilogram cabin. The result is 31.1 cabin. This is a positive result, which means that the temperature off the medium has risen. As you could see, the main focus is on deciding whether we have a closed system or an open system on determining the sign off the heat and the work. 13. 1st law of thermodynamics - Sample problem 2: Let's see another example. This time a fan is investigated, the family carries Air Withrow density and we don't flow rate. Steel medium is accelerated by the fan to see to speed. This means that the outlet speed is C two and the inlet speed is zero. As the steel medium has zero speed, we must determine the performance off the fan. The New America data is given. The density is 1.2 kilograms per cubic meter. The flow rate is thank you big meters per second and the outlet speed is 20 meters per second. Obviously, we should use the first low off Dama dynamics. But there are four creations. We should choose the proper form. The system cannot be considered as a closed system. The fan always carries different particles. We haven't open system as air or in other words, material goes through the family. So we need the recreation For open systems. We must consider the change off kinetic energy as the speed off air is changing. Therefore, the general form off the first law of thermodynamics should be used as that also contains the change of kinetic energy in this form, which is the entropy by itself, but the total on top e change equals to the some of the heat and the shaft work. This is a proper form, but or task is to determine the performance. Therefore, it is better to use the creation in performance dimension instead of energy dementia. Basically, the recreation is the same. We just differentiate by time. The energies can be written as mass times the specific in energies. The performances can be written as mass flow times specific allergies. This is the only difference we can calculate the mass flow, so we just need to determine the other quantities. The specific anti happy is related to temperature. The specific kinetic energy is related to flow speed and the specific potential energy is related to changes in attitude. The town's description says nothing about temperature change or attitudes change, so we can assume that these can be neglected. Therefore, the specific and 30 change that age equals zero as we neglect temperature change on the change of Spence if IQ potential energy danta e Foot equals 20 as we neglect attitude change. Besides, these heat rate is also zero, as the family does not transmit heat to the medium. It only transmits performers. We only calculate with heat rate for a family if it is specifically stated in the problem description or in practice if there is a noticeable heat transfer. Finally, there are only two terms in the creation. The kinetic energy rate on the shaft performance, the shaft performance is the performance off the fan that shabby determined. We can use the speeds to calculate the specifications. Antic magic change the kinetic energy equals mass times. Speed squared over two. The specific in attic energy is kinetic energy over mass, which means the speed squared over to the change can be written as the difference off specific in attic energies at the art plant. And in that the ant let means the later states. So we've right see two squared minus semen scrapped over to see even equals 20 as steel medium is located at the inlet, this steer medium is accelerated tube unknown sea to speed. The mass flow rate is the only unknown, but it can be calculated by taking the product off the density on the flow rate. All measures are known. We can substitute the powerful months off. The farm becomes 2400 bahts 14. 2nd law of thermodynamics - Entropy: similarly to the previous once. The second low is also an empirical axiom, so there are several possible phrasings. Mathematical E the one including an therapy, is the easiest to handle a classical phrasing off. The second law of thermodynamics is the close use principle. It is impossible for heat to transfer spontaneously from 1/4 to a hotter body without causing other changes. According to this, the energy transport has a dedicated orientation, even though the first love with a low any kind of energy transport. This better fits reality as heat voluntarily only goes from the hotter body to the Corder body. Another classic or phrasing means the impossibility off perpetual motion machines off the second kind. There is no period a caliph functioning machine or cycle that can do work just by extracting its Tamil energy. This also means that heat cannot totally we transformed into work. There is a need for some work input. This means you're Evers ability. Fauria processes the work can totally be transformed into heat, but the reverse off this process cannot be done. All of the heat cannot be transformed to work for mathematical phrasing. Off the second low, I must introduce an therapy in reversible and quasi static case. The differential heat equals to the product off the temperature and differential Entropy change. According to this, Cappy, 30 denotes the absolute temperature. As a matter of fact, the temperature is just defined at this point, but we still cannot determine a zero point so you can have a temperature scale. But you can't know it's starting point and therapy is marked by capital ass, and therapy is the measure off disorder. Small entropy value means an ordered state, and an therapy has a maximum at the completely disordered state, or thermodynamic systems tend towards the completely disordered state. For example, when the glass falls down and breaks, it will be less organized. This process cannot happen spontaneously in the opposite way. As you can experience it, I can give you a formula for entropy, but so far, please just think of it as the extensive state varietal off the timer interaction, which has to describe the direction of the time a dynamical processes. I would like to remark that the other formula is only through for reversible, quasi static cases. Quasi static means that the system goes under change through the Siri's off actual Librium states this assumption, the neighbors or calculations that we do in terms of dynamics in case of irreversible processes. There is an inequality instead of the actuality. The second law of thermodynamics in mathematical form states that, in case of spontaneous processes, the entropy off the isolated system can only increase off course. This doesn't mean that the entropy cannot decrease, but it requires energy input to do so. Entropy is an abstract notion, but I convention to formally related to it. First. The change of entropy is greater or equal to the different ensure he transfer over the absolute temperature. On the other hand, the entropy equals two minus one times the product off the boards, man constant and the natural logarithms off the Tama Dynamic Probability. I tell you this formula, just for the sake of curiosity, as we do not really use it in everyday engineering practice, The time of dynamic probability is a status ticker quantity, which means the probability off the current macroscopic state, the macroscopic state, means a possible energy distribution to which multiple micro states belong. The number of corresponding micro states determine ized the thermodynamic probability off the Mattress State. So Tara. Radically. By describing all possible states, you can determine the entropy, and therapy is always positive as the Luga rate is negative as the argument is smaller Dumbarton! 15. 3rd law of thermodynamics: the third law of thermodynamics have to set the zero point of temperature on an therapy scale, and again it can be stated in various forms. In the first form, The third law off thermodynamic streets as the entropy off a perfect crystal at absolute zero, temperature is exactly equal to zero in case off non zero temperature. The value off an therapy is a finished number. Let's translate. What does this mean? One autumn? Excellent matter can be considered Eskom politically ordered at zero absolute temperature, then they are freezed and they cannot even vibrate in case of molecules, the entropy is not zero at zero cabin temperature as they can freeze in multiple orientations during die rotation. In reality, we can experience that the matter has finished an therapy around zero Kavin, but the low is stated for the idea case. In another phrasing, I can say that it is impossible for any process, no matter how idealized, to reduce the temperature off the system to absolute zero value infinite number of operations. Basically the absolute zero temperature cannot be reached. Let me summarize the importance off the lows of Tama than the mixed in a natural. The first love. Time of dynamics presents the energy balance off the thermodynamic processes, but it does not say anything about the direction off the processes. The second low characterizes the direction off changes off state, and we can determine the absolute scale off the state for Aya birds by its help. But we cannot give a 0.2 these scares. The third low lets us to said the zero points of the scales, so we can finally described the temperature and entropy. Therefore, we can calculate with their help in case off anytime, a dynamic process. 16. Fun fact - Negative absolute temperature: I would like to share a fun fact in relation to the turd low. The turn low states that we cannot reach the absolute zero temperature, but it does not state that we cannot go into negative domain. This sounds controversial re, but the negative absolute temperature can be reached. Let me underline again that nothing can be at absolute zero temperature so that state must be avoided when we want to reach negative temperature. The temperature can be calculated with the help off the internal energy and an therapy. In this case, the temperature equals to the differential off internal energy with respected entropy at constant volume and quantity of material. This fulfills our physical sense as if the temperature increases both the internal energy and entropy increases to let's see how to get negative temperature. If the internal energy would change positively but the entropy negatively, then the temperature would become negative. As you can see from the formula, there is actually a really life example that has been experimentally shown in the fifties. In the classical example, there's a mine ethic field in which magnets are put the My nets are aligned with the magnetic field after enough time passed, then the direction of magnetic field is instantaneously turned to the opposite direction. The miners have no time to turn with the magnetic field, so they still remain in their original position. The internal energy increases greatly as the potential energy off the magnets are dramatically higher. In this case, compared to the previous case, the anthropic decreases as the new state is much more ordered than the previous one. As this state is further away from the actual Librium off course, this state is highly unstable and it collapses pretty quickly as the main nuts turn around . Interestingly, there is negative temperature and more interestingly, the temperature would never get to be zero. As it goes back to the positive domain, you can see the internal energy as the function off the temperature on the graph. You can see that the internal energy is greater in case off negative temperature values than in case of infinitely large temperature. As the internal energy decreases, the temperature goes in the direction off, minus infinity on the jumps to positive infinity to reach the positive domain, and it doesn't go through syrup. This seems to be very strange, but this happens only because the temperature is an unfortunate choice of perimeter. It would have been much better to use the reciprocal off the temperature. The graph is much nicer if we upload the internal energy. Is the function off the reciprocal off the temperature? This function has 1 to 1 relation with the temperature and even the entropy could have been described better with it. However, due to traditions, we used temperature that has the Viet property of being negative and positive while it can never be zero. 17. Ideal gas model: So far, the 10 month dynamic systems have only being investigated in an abstract manner. It's time to introduce more practical content for which gas models unaided. There are several gas models, the most often applicable. One is the idea of gas model. This model is only valid for sufficiently small pressure, which is usually through for the technical processes that you want to de of it. Or so the temperature must be considerably above critical temperature for the idea gas model. The critical temperature is the limit above which we can call the medium gas under the critical temperature record a medium steam. So we had going into details. The idea gas model is valid if the medium is gas and it cannot be used for steams off course there. Other mothers like the Rio Gas model for reach, the funder of US recreation stands. It is a better approximation off the rear process system. The idea. Gas model if the temperature is just slightly above the critical temperature, knowing this model is a topic off advanced thermodynamic courses. Now you can concentrate on idea gases as we mostly david them in the engineering practice. The idea of gas model contents. A couple assumptions this must hold for the investigating medium. Firstly, the volume off gas molecules is negligible compared to the total volume off the gas. This means that the gas is not to dance. Secondly, the only interaction among the molecules and among the molecules on divorce is the perfectly elastic collision here. The perfectly elastic collision is an approximation by itself because, according to that, not even a small part of the mechanical energy transforms into heat during the collision. Or so in reality, the miraculous attract and repairs each other. But now we need, like this effect. Totally. The temperature determines the ever its speed on the kinetic energy off the Monaco's. In accordance with the assumptions and the experiments, the most important relation off the idea gas model can be introduced. The E creation off state camp, written in multiple forms in the 1st 1 the product off the pressure and volume of the gas. It first the product of the amount of substance, the universal constant and the absolute temperature. The universal guests constant is the same for every gas. Its value. Its 8.314 Jewell Paramore cabin, usually the amount of substance is not known as we can rather measure the mass off the gas . According to this, we can rather use a form which includes the mass. Here, the right hand side changes. It is the product off mass specific gas constant an absolute temperature. The specific gas constant is a property off the given gas, and it can be calculated by dividing the universal gas constant by the molar mass. The mother must means the must one more gas, which is a material property as usually we cannot even determine the massive to gas if we don't even want to determine it. Therefore, there is 1/3 version off the idea. Gas low. The previous formula is divided by the mass. In the left hand side, the product of the pressure and specific volume is present. On the right hand side, the product of the specifications constant and the absolute temperature is taken. Oh firm. We used this formula so it's averted to remember 18. Relations in the ideal gas model: based on the idea gas model, the relations between the main quantities can be deducted. The following relations are only valid in case of idea gases as it's a proper mother. Usually these relations are good to know. I put them in pdf format and you can download them from the resource is so you don't have to write them down for yourself as a reminder. Let's go through the three forms of the recreation off state. The product off pressure and volume equals to the product off the amount of substance, the universal gas constant and the temperature or, in the second form, the product of pressure and volume. It was to the product of mass specify guess constant and temperature in the turtle on the product. Off pressure and specific volume equals to the product of the specifications constant and the temperature. It is important that the temperature is the absolute temperature which is substituted in cabins. There are four important material constants, and there are two independently creations that can be used among them. Therefore, if to material constants are known, the other two can be calculated. The four constants other following as a Barrick specifications, which means the specific eat at constant pressure on this mouth with CP Isil Correct specific heat, which means the specifications at constant volume on this marked with Stevie The specifications Constant, which has been introduced earlier and is marked with capital, are finally the Adia Batic index, or so called heat capacity ratio, which is marked with gamma. This constant is important in case of idea Batic processes. I introduced the too simplistic rations, which are valid. The first states that the specified gas constant equals to the difference off the ISA, Barrick and Isaac Orrick. Specific it. The second states that the idea Batic Index equals to the ratio off the ISA, Barrick and Isaac Orrick Specific it from the name heat capacity ratio. This can easily be memorized by def. Writing these e creations you can get formal A for calculating the ISA Barrick and Isaac Orrick specific heats, too. It is enough to learn these two e creations, and you can always get the others. By using these. It is voted to note that the eyes of our expensive thick heat is larger than the Isaac Orrick. So the specific CASS Constant is positive, and the Adia Batic index is greater than one. There are some formulae to calculate the change of Internet energy and answer happy too. The change of internal energy equals to the product off the mass. The Isaka expensive IQ, heat and the temperature change this camp of return for that Are you in case off in its changes? Or we can variety you for infinitesimally small changes. But mainly the formula is the same. Analogous. Lee. The change off specific internal energy can be calculated. You can see that the previous formula is divided by the mass on both sides. The change of an therapy is in similar form. The only difference is the use off the ISA Berrick specific heat instead of the ice. A correct one. Therefore, the change of anti P equals the product of mass Assab. Eric specific it and the temperature change. You can see that the change of anti P is always greater than the change of internal energy as the eyes uber expensive ticket is always greater than the Isaka. EXP ASIF IQ HEAT The change off specific and therapy can refund by dividing with the Mass similar to the previous case, just like in case of the change of internal energy and on top e a formula can be deducted for the change of entropy in its first form. The change of entropy can be calculated by considering that the entropy is the function of the temperature and volume. By dividing with the mass, we get a formula for the change off specific entre p. There is another form if we do not know the volumes, but we know the pressures. In this case, the entropy is the function of the temperature and pressure off course. The specific quantity can also be calculated. In practice, we use the first formula, including the volume in case off isil correct processes on. We use the second formula, including pressure in case of isobars processes. In these special cases, the ratio of volumes and pressures are one respectively, that for the logarithms zero, and we can calculate simply with the temperatures on the specifications 19. Definitions of special state changes: in this lecture, I got you to the definitions off Special state changes. These are important. Azriel processes can be modelled with the help of these special cases. State changes happen always if the intensive state for eyeballs are ingeniously distributed on the related. Interaction is not blocked by a four. There are several basic properties of state changes that you should keep in mind. We investigate quasi aesthetic processes, so the change happens through the Siri's off equilibrium states. In reality, only infinitely slow processes are almost quasi static. But using this assumption is fair for modelling purposes. The state of endpoints are investigated. The time dependence is not taken into account, which makes calculations much easier. There are two main categories off state changes. There are reversible processes in case off reversible processes. The change can happen in both directions, and the starting state can be reached by the rivers process from the end state. This means that if we change the state of the system and we do the exact same process in reverse, we get back the original state. So after arriving back to the original state, it cannot be noticed that the process even happened as boost. This system and the surroundings are in the same state as before. On the other hand, there are irreversible processes for which these statements are not true. Rhea processes can only get close to being reversible, but they are rather irreversible. In case of fria processes spontaneously, the change can happen only involved way and the starting state cannot be reached by reverse process. Energy dissipates so you can notice on the system and the surroundings that the process happened. Even if you get the system back to its original state, the surroundings cannot be in the same state as before. The first special state change to define is the ISA Barrick process. As its name indicates, there is constant pressure during the state change. This process can easily be created in practice. For example, a closed space with easily moving Christon works in an Isa Berrick manner. The outer pressure is constant and the inner pressure always equals to it to keep the acrid Librium off the pistol. In this case, only the temperature and volume changes. The next one is the ISA correct state change, which assumes constant volume, obviously a close space with fixed voice is a good example as the fixed wars does not let the volume change. In case off the ISA termer processes, the temperature is constant. It's harder to find an example for this, but in special cases, almost constant temperature can be kept. If you think of an infinitely slow process with he transfer between the system and the surroundings that have constant temperature. You can find that the change will be ice a term. A. There's enough time for the medium to transfer heat to stay at the same temperature as the surroundings. Already the name off the idea Batic process indicates that this is a process without heat transfer. Therefore, only mechanical interaction can happen every state for iBook and change, but they must change in a way to ensure zero he transfer from this condition. The relationship between the state Freiburg's can be deducted. Perfect insulation can be used as an example or even without insulation in case of an infinitely fast process. There is no time for heat transfer, so the change is a diabetic. The eyes entropic state change is a diabetic and reversible at the same time. Therefore, there is no terminal interaction, so the heat transfer zero. Because of the idea, Batic change or so the change of entropy zero as the process is reversible, for example, on infinitely fast process without closest can be considered ice and tropic. In case of poor, ultra big processes. There is no direct condition for any of the state for eyeballs every state where I ever can change. Also there can be boost thermal and mechanical interactions. However, there is a given connection between the state Mariah Bols, similar to the idea Batic case, the product off the pressure and the volume to the power off an is constant. This on is called the Police Tropic Index, and it's a material property that can be determined experimentally. Basically, every general area process is poorly tropic. If we choose the proper Polly Tropic Index, we can describe every special process that you learn so far as a poor little pick process. In case off Isa barrack processes and equals zero in case off isa correct processes on equals to infinity. In case of Isa Tama processes and equals to one in case of idea, Batic processes and equals two Gamma. The Adia Batic index last but not least there are eyes on topic processes. In this case, the entropy is constant during the process. This basically means an idea batting expansion without useful work. So there is an expansion without thermal interaction, and the useful work is zero. In practice, struggling is an Eisen topic process. Physically, you can imagine a flow in which there's a sudden change off the cross section, such that the cross section gets much larger. There are losses in this process without use Hoover or timer interaction. But why do we deal with such processes that mean only losses, for example, the cooling cycle content struggling as we need to lose some energy during that cycle? 20. Properties of special state changes: specials they changes have their own specific properties. This means that the generally creations take unit form for each state Change. These formulas are verse knowing I attached a summary off other important formula as a downloadable resource. Download it and make use off it. In this lecture, I only cover the most important properties. The others are only in the summary. In case off Isa Barrick processes the main property is the constant pressure. Based on that, the external work is pretty simple to calculate. Instead of integrating, you can take the product off the constant pressure and the change of volume minus one times . This product leads to the external work. The shaft work is even simpler. It is zero as constant pressure appears in the integral. In case off Isaac Orrick states changes, we can start from the fact that the volume is constant. The external work zero on the shaft were can be calculated quite simply, the product of the constant volume and the change of pressure gives us the shaft work. In case of ice it Irma processes, the temperature is constant. The consequence off the constant temperature is that the change of internal energy and unhappy is zero that leads to the fact that the external and shaft work are equal to each other on both of them equals two minus one times the heat. This comes from the first low off time of dynamics in case of constant temperature. The heat can easily be calculated by the product of the constant temperature on the change off entropy. The ice entropic state change is a diabetic and reversible at the same time. According to this, the heat transfer is definitely zero on the entropy changes zero to. From this, we can deduct a formula considering the relationship off the pressure and volume. The pressure multiplied by the volume to the power of gamma must be constant at all times. In case of political pick processes, there's given connection among the state for I a bus. This is similar to the formula off the ice entropic processes for patrol pick processes, the pressure multiplied by the volume to the power off. And it's constant where n is the police tropic exponent. This exponent can be determined for a given material by experiments. Besides this formula, there is no specific property of the police Tropics ST Change. Every quantity can be calculated according to its definition 21. Graphical representation of processes: In case of dealing with thermodynamic processes, we often used diagrams. This helps to imagine how complex process actually works on the virtues, and diagram also has physical meaning. You can mainly C two types of graphs in practice. In the 1st 1 the pressure is plotted as a function off the volume or the specific volume. The physical meaning off. Such graphs are connected to the area under the curve. In this case, this area equals to the work done by or done on the medium. Depending on the direction off the process, you can see these dependence on the example. If the medium expands, it goes from we've on volume to be two volume by the medium that's work on the surroundings . In this case, the work is negative. If the volume decreases, the work is done on the medium by the surroundings, so the work is positive. The curves off special state changes are very important. So let me get you through them. You can see the curves from each important state changes in case of idea gases. The isobars the lines related to isil berry processes are obviously horizontal. Similarly, the ice of course, the lines related to ISA. Correct processes are obviously vertical. The other three curves are basically representing the same relation. All of them are connected to the product off the pressure on the power off the volume in case off Isa Termer processes the exponent off. The volume is one to the ISA. Terms have the smallest steepness in case of ice entropic or Adia. Batic processes the exponent is around 1.4. In case of our in case of poetry pick processes, the exponent is depending on the medium. According to this, I only represented the police trope with a dashed line. It is not necessarily running under the ice and troops, but it could be also above it. I showed the case, but exponent off the politic process is greater than Adia Batic exponent. On the other main diagram, the temperature is plotted as a function off entropy or specific an therapy. In this case, the area under the curve equals to the heat transmitted to the medium or taken away from the medium. If the process goes from left to right, the heat is positive, so the heat is transmitted to the medium from the surroundings. If the process goes from the right to left, then the heat is negative, so the heat is taken away from the medium and it is transmitted to the surroundings. On the graph, the area cross hedged right words miss the positive heat that increases the energy of the medium. The area cross hedged left words means the negative heat that decreases the energy of the medium. That difference is the area off the rectangle, which means the tota he changed during the cycle. This heat is positive and it can be utilized for making the medium do some burke in the TS diagram. Obviously, the horizontal lines mean constant temperature or isa termer processes by the radical lines mean constant an therapy. So I Centra big or idea. Batic processes the isobars and ISA courts are similar to each other. But if an ISA bar and Isaac or goes through the same point, the as occur is always deeper than the Isa bar. The holy tropes have the shape like the one I indicated on the graph. However, the exact line always depends on the police tropic exponent. The two extremes off the poi tropes are the eyes and tropes and the ISA terms. However, you should just remember the main trends of the curves. It is useful if you want to understand the complex problems. 22. Piston – Sample problem 1: let me show you a problem related to pistons. The sample problem, perhaps the practice dealing with state changes in the problem. There is a pistol which can move without friction and has zero mass. There's actually bream in the state, which you can see on the figure. The cross sectional area off the piston is a the mass on the pistol is, and the atmospheric pressure is be note. The temperature of the gas is the one. It's mass is, um, gas on the material. Properties off gas are gamma and are you can see on the figure that the movement of the pistons it's constrained by ring, which is located halfway between the current position on the bottom. We must determine how much heat must be transferred to the gas. If we want to decrease the pressure to the half off its present value, the sun must also be considered. As obviously, the answer is negative, as we need to take it away from the gas to decrease the pressure, or Sylvie must determine how much work does the guests do and how much the change of internal energy and therapy and anthro pr. Finally, the whole process shall be re presented in PV and PS diagrams. The mass put on the pistol is that kilograms. The cross section of the pistol is 50 square centimetres. The atmospheric pressure is 100. Killer pass scans the initial temperature of the gases 40 degrees C, as is so 313 Calvins. The massive The Gus is one kilogram. The specifications constant is 287 shoe a pack kilogram Kavin, the diabetic exponent, is one point for First of all, let's think about the physical phenomenon and determine the state changes. The pressure shall be decreased. To do that, he transfer is used to decrease the pressure. The heat must be taken away first. The heat is taken away on the energy of the gas decreases, but the pressure cannot decrease. The inner pressure stays in actual Librium with the atmospheric pressure and the additional mass in the piece done to the inner pressure remains constant. So there is an ISA barrack process. The state changes Isa Barrick until the pistol reaches the ring. It can be seen from the German three that the volume decreases to the half off its initial value. Anti A that point from then on the volume does not change, even though he is still taken away from the system. There is an isil correct process because of the ring that blocks the movement of the pistons. The pressure decreases to half off its initial value during this process, so the desert and state is reached. We must go through these two processes. During the calculations. It is verse it to know the state reliables before and after each process. At the initial state the temperature was given, but the pressure on the volume is unknown. We must determine them to calculate the pressure. We can use the fact that there is an actual Librium. So the inner pressure off the gas keeps balance with atmospheric pressure and the gravitational force acting on the mask, which is put on the system. Soap, even pressure equals two p note, plus sometimes G over a. The gravitational force off the mass is distributed on the system, which has an area equal to capital A. That's why the second term is divided by a to get the pressure from the force. The initial pressure is about 100 manicure. Pasqua's the initial William can be calculated based on the idea. Gas slow in the idea guest low. Everything is known about the volume, so the volume becomes the product off, the massive biggest specific gas constant and the temperature over the pressure. It means 0.751 cubic meters. The first step is an iceberg process, so let's calculate the state for eyeballs after the iceberg process. The pressure is constant during the process, so the end pressure is still 100 particular Pasqua's. The volume is halved as we already discussed, so it becomes 0.375 cubic meters in case off Isil Berrick processes. The ratio off temperatures and volumes are the same. According to that, the temperature of the second state equals to the temperature off the initial states times the ratio off the volumes. This means 157 cabins. There is an ISA correct process in the next. Here the volume is constant, so the volume off the third state equals to the volume. In the 2nd 1 which is 0.375 cubic meters, the pressure drops the half off its in nature value. According to the problem description. Therefore, the pressure is 60 kilo Pasqua's the ratio off the temperatures and pressures are the same in case of Isaac Rick processes. Therefore, T three equals city to time speed tree over P. Two. So the ant temperature is 78 Calvins, which is a pretty low temperature. It means miners 195 degrees. As is, further quantities are easy to calculate based on the known states. Let's start with calculating the heat for that. We need to material perimeters that we do not know yet the Assab Eric specific it equals two R times come over Goma minus one. So it is 1005 Chua per kilogram cabin. The ASA correct specific heat equals to the as a brick specific heat over the Adia Batic exponent. It is 718 jewel parking program cabin. The heat transfer to the gas can be calculated now in the first step, there is an as a brick process from the first law of thermodynamics began that the heat equals to the change of an therapy as the shaft work is zero. So the heat for this step equals to the product of the mass. The eyes of Eric specifications on the change of temperature. In the second step, there's an ISA correct process. Again, we can use the first love Tama Dynamics. The heat equals the change of Internet energy as the external work zero in this case, so the heat equals to the product off the mass, the massacre, expensive ticket and the change of temperature. The result is negative. So, in fact, 200 14 kilo joule heat is taken away from the gas instead of receiving it from the surroundings. In the next step, we can calculate the work as the medium is in close place in the problem only the extent over Kasriel physical meaning. So that's calculate that we can use the special state changes the right a simple formula. In the first step, the constant pressure must be multiplied with the change of volume. According to the formula off the ice Barrick process the minus sign just three presents. The usual signed compassion to the work is positive If it is done on the gas in the second step, the extent of work it zero as there is no volume change altogether 45 kilos, your work is down the gas the positive result means that this work is really done on the system by the GUS is compressed. Let's continue with calculating the change of internal energy As the same formula stands for both processes. We can calculate the two steps together. The change of internal energy equals the product of the mass of the gas as a correct specific it on the total temperature change, it is minus 169 killers. You the same can be opened from the first law of thermodynamics. This is also good for checking. Go result. The change of Internet energy equals to the some off the work done on the GUS and the heat transfer to the gas. The change of anti pecan We've written in a similar form instead off the isil Correct specific it the Assab Eric one must be used so basically you can take gum. What times The change of internal energy. The result is minus 237 kilo joule. To calculate the change of Andhra P, you can also use its general formula by substituting the state varietals off the initial and end states. The change of entropy can be determined. Also, you can use the Isa Brick and Isaac Orrick processes. There are two e creations for the change of entropy in one of them. The term, including pressure zero for ice Obrecht processes in the other VON the term, including volume zero for ISA Correct processes. You can get the formal of Rita here. Either way, the result is minus 1000 194. Julia Parker oven Finally, let's blow the processes. Every data is van known for the PV diagram. The initial pressure and volume can be found from their volume decreases to half off its value in the first step. By the pressure, it's Constand. In the seconds that the volume is constant and the pressure is halved, it is a pretty simple diagram. In case of the TS diagram, the temperatures are known, and also the total change of entropy is known. The first section is as a brick. On the second is Isaac Orrick, so the 2nd 1 has greater steepness. This shabby reflected on the figure, but the exact shape off the curves does not have to be found 23. Piston – Sample problem 2: Let's see another example of it a pistol. There's gas in a closed space covered by a frictionless. Based on. This means that the volume can change without any loss due to friction. The initial temperature and pressure off the gas is now from this initial state. The gas is very quickly compressed to the third off. It's only Gina volume. The creek compression means that he'd change cannot occur during this process. This kind off language indicates that the first process is eyes and traffic. After the compression, the piston is fixed and the pressure of the gas is raised toe Petri by heat transfer. As the pistol is fixed, the volume is constant. The second process is Isaac Orrick. We also know that the mass off the gas is, um and it cannot change during the process as the system is closed, or so we know to material properties the specific gas constant and the idea Batic exponent . They must determine the amount off work which is done on the gas during compression and during the whole process or so. Vinnie, the Tota heat transfer, the worst, the guests and the total entropy change. Finally, we should draw the whole process in PV and TS diagrams. To do this, we must calculate the main quantities at the beginning and end off each step. The initial pressure is 100 kids off Baskins. The initial temperature is 293 cabins. The pressure at the end state is 700 kilos. Pass cars. The mass off the gas is 0.5 kilograms. The specific gas constant is 287. She was sparked kilogram cabin and the other batting exponent is 1.4. We can identify the physical phenomena based on the test description. First, there is a quick process during which there cannot be any heat transfer. This indicates an ice anthropic process. The heat is zero as there is no heat transfer, or so the entropy changes zero in case often as entropy process. Besides these, we have additional data related to the compression. The volume is decreased, the third off its original value during the compression, so V two equals two Beavon over tree. Based on these information, we can calculate everything for the eyes. Entropy process after the eye Central big process. The volume is constant as the Kristen is fixed therefore on Isaac. Correct process takes place. We three equals to read too. The pressure off the end state is given. It is Petri. This enables us to determine the other variables at the end state. Now let's go through all the processes. First we have to deal with the initial state. We don't know the initial volume, but we do know the value of every other important reliable. Therefore, there is only one unknown in the equation off the idea gas low. We can express the volume by the half of the mask, the specific gas, constant temperature and the pressure. The initial volume is 0.42 cubic meters. Now we fully know the perimeters at the first point, we can continue with the second. The second state is the one after the ice entropic process. The volume is the third off the initial volume, which means 0.14 cubic meters. This property has been the easiest to calculate. From now on, we should consider the type off the process, the eyes entropic in creations, shabby used. We can calculate the pressure in the second state, the product off the pressure and the volume to the power of the Adia Batic exponent is a constant in case of an ice entropic process. P two can be expressed a speed even times or even over wi due to the power of gamma. The pressure equals to 466 killer Pasqua's in the second state. We still need the temperature in the second state that is the last unknown varietal. In such a case, we can use the idea gas low. The master remains constant. As we have a closed system. P to be to r M are known. The temperature in the second state becomes 454 cabins. At this point, we fully know every important later about the second state. Now we can go on to calculate the properties off the end state. There is an isil correct process between states to entry. The volume remains constant, so we treat equals to read to. The pressure is given at the on state, so the only unknown is the temperature. This can be expressed from the idea gas slow, just like before. Now I use an other immigration in case of an ISA correct process. The ratio off temperatures and the ratio off pressures are the same. T three over t two equals two Petri over pt by rearranging tea Tree is t two time speed tree over P two Numerical. This means 682 cabins. Now we finally know every important state friable in the three states. We can calculate anything but usual recreations. Let's start with the work during compression. The compression was the first process. It has been an ice entra big process, which means that the heat transfer is zero. If the heat transfer is zero, the first low off thermodynamics becomes quite simple. The work can be expressed by the temperature change. We have a closed system as the piece done closes a cylinder. This means that we should use the first law of thermodynamics for closed systems. Therefore, the work equals to the change of Internet energy within the second on first states, actually, there would be heat added to the work. But that's now zero. The change of Internet energy equals to the product off Isakovic specific heat mass and temperature change the massacre. Expensive ticket is unknown, but we can easily calculate it as usual. The as a great specifications equals to the quotient off the specific gas constant on Goma minus one where gamma is the idea. Batic exponent. Now we can substitute and find out that there is 57.8 killers Your work on the gas during compression as the energy of the gas rises. This work is certainly positive. Let's calculate the total burke. The second process is ISA correct. We should calculate the work according to the A security creations. If the volume Ms Constand, the work is always zero. This is obvious based on the definition off bird. Therefore, the total work done on the gas equals to the work which is done during compression. Let me note that you should always check the data's off the question. They asked for the work done on the gas. This appears in the creations. Naturally, If they ask for the work done by the gas, you should multiply the results by minus one. We can continue by calculating the heat transferred to the system. This is the heat that appears in the first low off thermodynamics. We can calculate this for every process. The heat transfer is zero during the eyes entropic process. According to its definition, we have already acquired this information. The heat transfer during the ice a correct process is still donated. We can certainly use the first load off thermodynamics. There is a closed system for which the Internet on magic change can be calculated on. The work is already now for this second process. The work is zero as the volume is constant. Therefore the invasion gets fair. The simple The heat transfer equals the change off the internet energy. We can use the usual formula 81.9 closures off heat is transmitted to the gats by the surroundings. The last thing to calculate is the entropy change. We need the total entropy, but we should can't lay the entropy for each step. It is better now. The entropy is constand during the eyes and Trawick process, so the entropy changes zero. There is a non zero entrepreneur change in case of the isil correct process. There are two formulas that you can choose to calculate the entropy change rate. It is better to choose the bomb which contents William change and temperature change. As the volume change drops out, however, you can use any of the formulas by substitution the result is 146 Jews over cabin. The total entropy change is the sum off to entropy changes. It equals to 146 Jews over cabin, the PB and T as diagrams should be thrown. We know the states, so we haven't easy task. Let's check the PV diagram. First, you can mark the 1st 2nd and third state at the Williams, and pressures are no from the first state, and I central big process takes us to the second state. Then an ISA correct process connects the second and third states. So we continue with straight vertical line. Let's see the Tia's diagram to We did not know the entropy values as only entropy change can be calculated. We can mark the three known temperature values. We know that there is no entropy change between the first and second States, and we know the exact value off the entropy change between the second and third state. The first line between points one and two is simply a straight vertical line. From point to 2.3, you should drew an isil core 24. Complex process - Sample problem: Let's see a general complex process which consists off multiple state changes. There is nitrogen gas, which can be considered to be an idea. Guess the specific eat off the nitrogen is constant. The initial state has fever pressure and de even temperature from this state. The against is heated to T to temperature. Meanwhile, the pressure stays the same. Therefore, the first process is Eissa Barak. Then the gas is expanded to be three pressure in India, Batic and Reversible Manner. This means that the second process is ice and traffic. Both the heat transfer and the entropy change are zero. In the second process. As the material properties the moon, our mass and the idea Batic exponent are given. We must determine the specific value off the work the shaft work, the heat, the internal energy change on the Antarctic change for the whole process. The in the shop pressure is six bars. The initial temperature is 300 cabins. The temperature after the as break stayed change equals to 443 cabins. The end pressure is one of our This occurs after the ice entropy process the moon. Our mass off nitrogen is known If it is not given. We still know it from the periodic table. Also, the other robotic exponent is known, so we have to material data. From this, we can calculate all of the other material data. With the half off the mother mass, we can determine the specific gas constant. The crew shins off the universa gas constant on the moon. Our mass equals the specified just constant. The universal gas constant is a known constant. It always equals to eight hours and 314 Jewish over killer. More Kavin be ever off the June It's the moon. Hamas was given in kilogram per kilo more unit, so we need the universal gas constant and shoot over Killam or Cavin unit. The specific guess constant off nitrogen is 297 shoes, par kilogram Kavin. We can also calculate the other two important material properties as usual, the Isa Beric and as a quick specific heat can be expressed by the help of the specified grass constant and the Adia Batic exponent in the upcoming calculations, we need these properties. Let's summarize the sub processes off the complex process. Now there are two steps. First, there is an Isa Berry process. The pressure stays the same ride. The temperature is increased, so the pressure at states one and two are the same by the temperature. Changes from TV want to t two. The temperatures and the initial pressure are given, so we basically know the initial on and state of the ASA Barry process. As the pressure and temperature are known in the endpoint of the process, we can calculate all other variables at the end points. The second process is ice and Tropic. As it is, both Adia, Batic and Reverted Bill the specific heat it 1st 0 according to the idea Batic manner of the state change or so the specific entropy changes zero according to the river cyber manner. Off the process, the gas is expanded, the pressure changes, the pressure of the end state is given and we have just expressed be to pressure. T to temperature is also known, so we just need to calculate t three in order to calculate any measure related to the process. So we only have to calculate the an temperature off the ice entropy process. There is a connection between the temperature and pressure ratio in case of ice entropy processes as only tea tree is unknown. We can express it. T three equals two t, two times the proper exponent of the pressure issue. The numerical result is 266 Carrion's. Now we have the last necessary data. From now on, it is just a formality to calculate necessary measures like the specific value of the work , that he'd the Internet and you change order under change. Let's start by calculating the specific Internet energy and anti change. These have universal formula. The specific Internet energy change equals to the product off the as a correct specific it and the temperature change. This formula could be used separately for the sub processes or we can use it for the whole process as the temperature is decreased, the Internet energy change is negative. The specific inter and that change is minders 27 0.5 kilos Jewess Parking program. The specific Antebi change in first to the product off the as a very specific it on the temperature change numerical E. After substitution, it is minus 38.5 kilos use per kilogram. Actually, we could calculate the specific antibody change from the specific Internet energy change by multiplying it with the idea. Batic exponent, This equation is true as the answer Barrick Specific ID equals to the product off the other robotic exponent on the ice. Incorrect, specific eat. We can calculate the specific eat to hear the formula is not universal. We should rather choose the proper form off the first low off Dermot Dynamics, as you know, the some of the heat and the work equals to the Internet energy change. But you can also use the other form of recreation, which states that the some off the heat on the shaft work equals to the entropy change. You can defend virtual shaft work even if the process is closed, or you can define virtual work even if the process is open. The in creations steel stand in case off as Albert processes the shaft. Work zero. As the pressure does not change, the first law of thermodynamics for Open systems Dan's you that the specifications equals to the change off specific toppy. The specific answer. Be changed between states want and to seek first the 145.6 killer Jewess Pai Kilogram. The second process is eyes entropic. This means that the process is Adia, Batic and reversible the specific. It is zero for another robotic process, so we do not need to calculate anything. What together the specific heat equals to the some off the specific hits, which means 145.6 killer Jewess per kilogram. The result is positive, so this heat is transferred to the system by the surroundings. Finally, we must determine the specific work on the specific shaft work. Once again, we should use the first law of thermodynamics. The specific work appears in closed systems and the specific shaft work appears in open systems. The specific work equals to the difference off the specific Internet energy. Change the specific heat as the some of the heat on divert it first to the Internet and you change the daughter. Specific word equals tu minus 173.1. Does you respect program? The specific shaft work equals to the difference off the specific entropy change and the specific he'd as the some off the shaft. Work on the heat equals to the antelope change. The total specific shaft work becomes minus 184.1 kill a Jewess per kilogram as the work and shaft work on negative, the work is done by the system on the surroundings. 25. Polytropic state change – Sample problem: let me show you a sample problem to learn how to calculate in case of political big state changes. The problem is the following the pressure, temperature and volume off Agus in a given space closed by a friction honestly moving east on are known. This is state number one. The gas is compressed in poorly tropic manner to estate with known pressure and temperature . This is state number two. The gas can be considered idea. It's specific. Heat is constant. The idea Batic expert and the specified gas constant is given the police tropic exponent. The heat transfer to the gas and the work done on the gas must be determined in the 1st 8 The pressure is 100. Killer Pasqua's the temperature is 100 drink tea statuses, which would be converted into 373 Cavin as it's rather used in the creations. The volume is 0.1 cubic meters. In the second state, the pressure is 150 killer Pasqua's and the temperature is 413 cabins. After the conversion from the material properties, the idea, Batic expert and gamma is 1.4, and the specific gas constant are is 287 shoe a packet of drum cabin. Let's calculate the political pick exponent. First, we can use to e creations to start with three times we to the power off, and it's constant as we deal with the police exchange of state P times we over tea is constant according to the idea of gas low. So there are two e creations that we can write between state number one and two Only the pressure and temperature unknown in both states on the volume is known in the 1st 8 So the volume of the second state shabby, dropped out of the creations. Let's take the creation on the right, which refers to the idea Gas low, raise everything to the ant proper and divided by the recreation on the left. After transformations, we get the DeRay Chios off temperatures equals to the ratio off. The pressure's to the power off on minus one. Over on From this equation, the police, Tropic explained, can be found. It can also prove to be useful to know this e creation, as it appears quite often in problems. Also, the ratio off the Williams can be connected to the other ratios for that, the original creations shall be divided by each other. The most important is to know that the ratios of state for eyeballs are connected. That's the orbital recreation. The logarithms off both sides can be taken according to the identity. The exponent inside the logarithms can be taken out as a multiplier. It is very useful trick on the just in time of dynamics. Keep it in mind. Now it is enough to do some transformations. It is not easy to see, but you can do it step by step at the end. The politic exponent is 1.34 which comes from the e creation that you can see. Because of the close system, external work shall be calculated. There is no specific formula. So we must start from the definition to get the external work. The pressure shall be integrated is a function off. William. We know the initial volume, but we still need the volume of the in state. The volume of the in state can be calculated in two ways. The first equation comes from the idea guest low on the second comes from the creation of the politic process. You know, frumpy times we to the power of and the Quester constant number. Anyway, we gathered. The pressure is 738 10,000 cubic meters. To calculate the integral Mystere need the pressure as the function off volume. Let's use the equation off the police tropics ST change on the left hand side, the general pressure and for you, miss present On the right hand side, the pressure and volume off state number one is used From this you get that the pressure equals to people. In times we want to the power off an times the volume to the father off minus. And here he is the pressure which depends on the volume We even and even have known values . So the pressure it first there constant times the volume to the power off minus the pressure function can be substituted to the definition off the extent of work. The constant can be put in front of the integral. The integral camp taken, you can integrate as a polynomial, so the excellent becomes greater by phone and then you must divide by the exponent. After that, the substitution of 32 and even can be done at the upper and lower integration and the New America results can be calculated. Finally, I did one more transformation to have a nicer result. But you don't really have to do that by substituting into any of the creations you get. The work is 3147 shughur. The result is positive as work is done on the system. During compression. The heat transfer can be calculated by the half of the first law of thermodynamics. The first low is Valium. For close systems, the change of internal energy equals to the some off the heat and the work. From this, you get that the heat requested difference off the change of Internet energy on the work. We already know that work. The internal energy can be determined by an alternative formula. It is the product off the esoteric specific heat, the mass and the change of temperature. Still, the other coric specific it and the must are unknown. The esoteric, specific heat can be calculated by the help of the other guests properties. There are two known a creations between the material properties. The specifications constant is the difference off the Isa Burke and I securing specific. It's on the other. Robotic expense is the ratio of them. From these, you can get the as a correct specific heat equals two R over gamma minus one. It means 718 Jew, a par kilogram cabin. The mass can be calculated from the idea of gas low. Let's use the initial state, the product of the pressure and volume equal to the product off the mask, the specific cast constant and the temperature from this the mass can be calculated. It is 935 10,000 kilogram. Now we can calculate the heat by the creation that we already determined is now. We can also calculate the change of internal energy minus 464. Jewel here is transferred from the surroundings to the system. So in fact, 464 jewel heat is extracted from the gas and it is given to the surroundings. The poetry big process is a good approximation off reality. So this is what really would happen. In such cases, the results can be plotted diagrams. We know everything to draw the curve on the PV diagram. In case of the tea as diagram, the entropy values are unknown we can only mark the temperatures on. We can throw the constant pressure lines accordingly during compression. The temperature increases by the gross is a cure, as the change is not reversible. Important a case Because of the universe abilities, there is a positive entropy change, so the curve tends Wright's words. 26. Efficiency: Even though energy doesn't disappear during processes, efficiency must be defined. There are actually a couple of definitions, all of them compact area process to an idea process. The first important quantity in the topic is the timer efficiency. The Tamela efficiency equals to the performance over the input heat flow. Here, the performance is an outward performance, which can be extracted from the cycle. In OptiMark case, the Toyota heat flow could be transformed into useful performance, but we know that it is not possible according to the second law of thermodynamics. Despite that, the optimum gives a good basis for defending efficiency. Absolute values appear only to make the definition easier. In this way, we do not have to think about san conventions. The main point is to get the ratio off the useful quantity and the in food quantity. The useful performance is the difference of the incoming and outgoing heat flows, so the efficiency can be written only by the half off. The heat flows on the diagram. The upper line is connected to the incoming heat, and the bottom line is connected to the outgoing heat flow. This is the consequence of the directions of the processes if the efficiency is not written by the help of the performance, but with the help of the work and the heat than the clothes. Rectangle on the diagram means the heat, which can be extracted and used as a useful work. The area gross hedged right words means the incoming heat and the area crow. Such Lefferts means the outgoing heat. This is a simple diagram, but you can think in the same manner in case of more difficult cases. The terminal efficiency gives us a good starting point as it describes the efficiency off the processes. However, in case off reality, we can guarantee lossless processes for further description. We must define the efficiency off each process. The US entropic efficiency can be defined. It compares the rear process to the idea of on in case of turbines. We want to extract work from the energy of the medium. The eye central big efficiency off a turbine is the ratio of the Rio change of anti P and the idea change of anti happy. In the idea case, we can extract a given amount of energy, but in reality we can extract less. This is characterized by the ice and tropical efficiency. This efficiency can easily be understood by looking at the ts diagram. We start from hype, even pressure state, and we expand the gas until P to pressure in the idea case idea batik reversible expansion happens which would end a T two idea temperature as the change of entropy is zero. In reality, there are irreversibility ease losses. So even though reach P to pressure, the temperature is slightly higher. In this case, there is a positive entre pre change. As the temperature change is proportional to the change of entropy, you can see that the rial process has smaller and happy change than the idea process, so we can extract less use for the energy from the turban. Compared to the idea case, the eyes entropic efficiency is similar in case off a compress. Or however, in case of a compressor, we don't extract any useful mechanical energy. But we need to use mechanical energy to power the compressor on increase the energy off the medium inside. So the efficiency is the ratio off the idea on the rial change of an toppy, but the idea of an shall be divided by the re of on. There's a given amount of energy that we need to introduce to the system in the idea case. But in reality we also have to cover losses. So we need more input energy. You can also see this on the diagram. We start from the lower pressure lever. We compress the medium from P one to p two. Pressure in idea case, we only increase the temperature to t two ideal temperature. If there are losses so positive entre pre change occurs, we need higher and temperature to reach p to pressure. This needs additional energy in boot. Let me summarize the ice entropic efficiency. You can see that the idea on the rial Antebi changes switch base in the two e creations. However, it is very logical how to calculate in case of turbines, we want to extract energy. Meanwhile, in case of compressors, we put energy into the system. Make sure to use the proper formula for each case and remember the differences 27. Turbine – Sample problem 1: after the introduction to all kinds of efficiency metrics. You can deal with any turban or compress, or let's see a sample problem related to turbines an idea Gus enters a turban with given pressure, temperature and velocity. The process taking place inside the turban can be considered to be a diabetic. The exiting medium also has known pressure and velocity, but output temperatures are known. The area of the cross section at the section and is Avon the specific gas constant and answer Barrick specific heat are the given material properties. The high difference between the two answer to turbine is negligible, so we do not have to calculate with the potential energy the chef there, four months off, the turbine is also given. We must determine the temperature of the exiting us, so the output temperature or so we must determine the entropy production rate during expansion and the US entropic efficiency off the turbine. The problem that Scripture stated that the process is Adia Batic, but it hasn't said that it is reversible. So the state changes not as entropic. The entropy increases. The input pressure is 800 killer Pasqua's. The input temperature is 773 Gavin after conversion. The input velocity is 90 meters per second. The velocity is marked by sea as we is already taken as a denotes specific volume. The input cross section is 50 scarf centimeters as the section and means that input. The outward pressure is 100 radical. A Pasqua's on the adversity is 140 meters per second. The specific Gaskell stand is 200 Europe a kilogram Cavin the as a brick specific. It is 550 Jewess per kilogram cabin. The shaft performance is 400 kilowatts. We cannot calculate the outward temperature just by knowing the pressure ratio and the input temperature, as we must calculate, with the velocity change between the two states. According to this, we can only calculate based on the first love family dynamics and suppose the temperature on velocity change appears there. The first law of thermodynamics is used for an open system in Adia Batic case at flow rate dimension. So the total anti P change appears the heat flow rate is zero and the other specific entities are multiplied by the mass flow rate to get the proper dimensions. The change of potential energy can be neglected. The performance of the turbine is marked by the index capital T. It is minus one times two given shaft performers. As the performance of the turban is extracted from the medium, it shows how much the useful output performances. The performance would only be positive if it increases the energy of the gas. That would be the case of compressors, but the work is done on the medium. The change of specific and therapy can be written as a product off the ice Abric specific heat on the temperature change. The change of specific kinetic energy is the difference off the second power off the value cities over to in this e creation, T two appeared. We want to calculate it, but we still don't know the mass flow rate. We need the density to calculate the mass flow rate. The density is the reciprocal off the specific volume, which can be calculated from the idea of gas slow. The input state is completely known, so we can calculate the density at that state by dividing the pressure with the product of the specific gas constant and absolute temperature. The density is 5.17 kilograms per cubic meters. The mess low rate can be calculated by the half of the density. The mass low rate is the density times the volume flow rate, which equals to the product off the input diversity. On the imp across section area, the result is two point territory kilograms per second. The first love, Tama Dynamics, can be used to calculate at what temperature it becomes 470 von Calvin's, which means 198 degrees says is there are two e creations for calculating the specific an therapy. As now we know the pressures on the iceberg specific heat. It is better to use the one containing them instead of the one using specific volumes. According to this, I calculate anti reproduction rate by multiplying the specific entropy in the mansion form by the mass low right. The specific entropy is the as a very expensive fiqi. Times logarithms off the ratio of temperatures minus the specified gas constant multiplied by the logarithms off the pressure ratio. The result is 249 votes per cabin, so naturally the entropy increases because of the Year of arse abilities. The US entropic efficiency off the German can be calculated based on the van in the creation. It is the ratio of the rial on the idea change of unhappy in both of them. The iceberg specific. It is more replied with the temperature change so we can forget that multiplier on. We can calculate just by using the temperatures in idea case the and temperature off. The expansion is lower than in case of the Rio case as the universe abilities increased the and temperature. To get the solution, we need to know the and temperature off the idea case. It can be calculated by the help of the entropy production rate in idea case, the process is reversible, so the entropy production rate is zero. We can use the recreation that I showed you before, only the idea and temperature shall be used instead of the rial on temperature. By rearranging the terms we get the idea and temperature is 316 8 cabins, which is about 100 lower than the rial on temperature. Because substitute into the efficiency formula, the result is 74.6% which is not a very good value. It seems like the antibody production is quite great in this case, 28. Turbine – Sample problem 2: Let's see another example, including a turbine. An idea Guess enters a turbine with given TV on temperature and exists with T two temperature after an idea. Batting expansion. The efficiency off the turban is eat. 30. How much does the entropy production changes if the Internet turbine efficiency changes to eat 30 comma. The kinetic and potential energy change is negligible in this problem, and we know that the performance of the turbine is w chef dot. In both cases, the temperature at the entry is wanders and degree SAS is on. The temperature at the exit is 400 degrees, as is. This should be converted to Calvin's. The original efficiency is 90%. This increases to 92 person. The shaft bear four months is 500 kilowatt. We do not know the pressure or material properties, so we cannot really calculate the variables at each state. We need to simply fire work. Certainly, entropy production must be calculated. In other words, this is the intrepid rate, so we should use the formula for intra pure and cooperate. The Inter operate depends on both the temperature and pressure issue. Off the process, however, the pressure ratio is unknown. But we do know how the process can be modeled in case of a turban, the initials that it has greater temperature and pressure from this state. The gas bills through an idea Batic expansion to a state with lower pressure and temperature value in idea case. The other body expansion is also reversible, so the process would be ice entropic. This ascent tropic process would mean a straight of article line in the TS diagram. Compared to this, there is a finite entropy increase in reality as the process is not reversible. The rial and state has how your temperature than the ideal and state, but the end pressure is the same. This is what we can use in our calculations. The process between the initial temperature and the reversible and temperature is eyes on traffic. The anti operate zero in an ice intra big process. The entropy does not change. This is what an ice interview process means, so we can go from T von too t to ideal with zero androphy production. Let's use this. We do not calculate. Director between Teavana anti to riel refers good t two ideal and then we go to T to riel from T two idea. Therefore, we just have to calculate the anti operate between the ideal and the rial endpoints. These are on an ISA bar. The pressure is the same for down as the pressures are the same, the pressure ratio is one and the inter operate formula gets simpler. The anti operate off the known eyes. Entropy part can be calculated purely based on the temperature ratio. There would be an other expression with the pressure ratio, but that it was zero. If we go on an ISA bar, I know that this is quite theoretical, but we needed to consider the background. From now on, we can just calculate, based on this immigration, the turban efficiency and the shaft there for months. Let's use the turbine efficiency first. The internal efficiency equals did the ratio of the rial and ideal on top changes. This ratio can be expressed by the half off the temperatures. We know the initial Teavana temperature and the realty to and temperature these are given. We also know the efficiency of the turbine so we can express the ideal and temperature. The idea and temperature off expansion equals 2 606 Gavin's If we calculate with the original turbine efficiency, the shaft performance can also be expressed by the temperatures, the product off the mast rate, the iceberg specifications and the temperature change equals to the shaft performers. The product is actually the entire period, which equals to the shaft performance as the heat rate is zero in case often Adia Batic expansion. Anyways, we must calculate the mass flow right on the eyes of our expressively hit. As they appear in the entropy formula. However, we do not have enough creations to determine both of them, but at least we can calculate their product. The product off the mass flow rate and iceberg specific kid equals to 800 33. What over cabin? As this product appears in the answer operate formula, we can actually calculate the interview production. Now. We consisted to the multiplier and the temperatures into the inter operate formula. We only calculate between the real and ideal and temperatures as we know that the answer parade between T one and T two riel is zero. As we only calculate from t two rial to t two ideal, we must substitute the rial and ideal temperatures into the general former. The anti operate equals to 87.4 Once over cabin, this equals to the total inter operate between Steven and the rial and temperature. We have calculated the anti operate in case of the original official See, we need the difference off the anti operates for the two different officials is so we must be the same. Calculations for the new efficiency value to the initial temperature on the idea on temperature remains the same, but the rial and temperature changes as the efficiency changes. The increased efficiency actually means that the rial and temperature gets closer to the idea. We can use the formula of the turbine official savants again. This time the rial and temperature is unknown. We can express it. The new riel and temperature is 659 cabins by increasing efficiency and temperature decreases, as we would expect that it is still on the ISA bar. The same eyes a bar that was in the first case, the shaft bear four months remains the same according to the test description. Otherwise the performance would change, too. Now the performance is the same, So the product of the mass flow rate and Assab Eric specifications must be different. The product equals to 814. What over Calvin? In case off the new efficiency value, we should substitute this new value into the answer. Operate formula. The same formula can be used as before. The multiplier off the logarithms on the rial and temperature mean the differences. The new value of the anti operate is 68.2 watts Bar cabin. Therefore, the change off entropy production is miners 19.2 once per cabin. As we increase the efficiency, the answer operate decreases by 19 to what's better. 29. Compressor – Sample problem 1: Let's see a sample problem with compress or to air, enters a compressor with given even pressure, even temperature, and see one velocity. The exiting air also has known pressure, temperature and velocity are and gum momentary of properties are given. The height difference between the two aunts of the compressor is negligible, so we can forget about the change of potential energy. The compressor is cooled with a given coding performance on its shaft. Performance is also given. The ones determine the mass flow rate off the air, the entropy production rate during the compression and the eyes entropic efficiency off the compressor. The properties off the input and output are Verne known. The input pressure is 100 killer Pasqua's the temperature is 292 canyons and the velocity is five meters per second. The outward pressure is 900 killer Pasqua's the temperature is 592 cabins and the velocity is 80 meters per second. The specifications constant is 287 us back. It'll Graham Cavin, the idiomatic exponent is one point for the cooling performance is 20 kilowatts and the shaft performance is 200 kilowatts. The calculation off mass flow rate could be done by the half off the density velocity on the geometry. The mass flow rate equals the product of the density and the volume flow rate. So the product of the density the cross section area on the flow velocity. This is true for both the input on al pretend. But the jail math three is not given, so we cannot calculate like this. The only thing that we could calculate is the density, as it is the reciprocal off the specific volume. So it is the pressure divided by the product of the specified gas constant and the absolute temperature. We need an alternative matter to calculate the mass flow rate. The mass flow rate also appears in the first law of thermodynamics. If you write it with the performances here, everything else is known. The first love, Tama Dynamics shabby, applied to an open system, is air goes to the compressor. There is material flow in and out or so we need to use the total and therapy as the change of kinetic energy is not negligible. Just the change of the potential energy, the performance acting on the medium, the air equals to the shaft performance of the compressor as it increases the energy off the medium. However, the heat flow is negative as it is given a schooling performance, which means that the heat is extracted from the medium. We can substitute the formulas for the specific and API and the specific in attic energy. The first term is the product of the as a brick specific eat on the temperature change. The second term is the half of the difference off the velocities. Scratch the as a very expensive ticket can be expressed by the half of the other material. Properties are Times gamma over Goma, minus one week, first wanders and five shoes par kilogram cabin, which is the usual result for air. The mass flow rate can be expressed now and everything can be substituted. The result is zero point 632,000 kilograms over second. The entropy production rate can be calculated in two ways. As the specific answer become, we've written with half of the temperature, aeration pressure ratio or with the help of the temperature ratio and the specific volume ratio. Now it is better to use the formula with the pressures as we know them. After substitution, we get that 49.3. What's back Alvin is the entropy production rate. It is positive, so naturally the entropy increases because of the irreversibility is as we don't do anything to decrease the entropy. I already showed you the formula of calculating the ice entropic efficiency of a commercial . So let's just use it. The ratio of the ideal and really entropy change is the efficiency. It can also be returned with the half off. The temperature changes, so let's use that form in idea case. By increasing the pressure, the temperature increases to give them point. However, in the Rio case, the universe ability is increased the temperature further so there is a higher and temperature. The idea, or reversible process, can be calculated by the half off the zero and ropy change. We use the formula for the entropy production rate. In the previous task. We can use that as we know that it's value is zero and we can calculate ideal and temperature. However, there is an alternative solution to the temperature ratio off a reversible compression. Can we've written by the half of the pressure ratio, the ideal and temperature ratio equals to the pressure ratio to the power off gamma minus one. Over. From this, the ideal and temperature can be calculated. The result is 549 cabin, which is clearly lower than 593 cabins for the re our case. By substituting in the efficiency formula, we get the efficiency. The numerical value is 85.3% which is a realistic result in case of a compressor. 30. Compressor – Sample problem 2: Let's see an under sample problem with a compress, or this time air enters an insulated compressor with give them even pressure, even temperature. And we don't flow right as the compressor is insulated. Heat transfer is not alone. The heat rate is going to be zero. The pressure at the outlet is be, too. We also know the geometry. The inlet and outlet cross sections are a farm on A to the outland is located higher than the in Latin. On the height difference is that a C. The efficiency off the compressor is at sea from the material properties, the specific grass constant. On the other aerobatic exponent argument, we must determine the density off air at the inlet and outlet, and then we must determine the shaft performance of the compressor, which actually means the mechanical form us. The in that pressure is 100 killer past cans. The inlet temperatures, 15 degrees senses and the in length cross section is zero point funds square meters. The outlet pressure is 700 killer Pasqua's. The other temperature is unknown on the Antarctic Cross section is 0.5 square meters. The flow rate off the air is 50 cubic meters per hour. This should be converted into cubic meters per second. Simply, we divide by 2600 as we've right seconds instead of ours. The height of difference between the in Latin and out. That is two meters and you must remember that the outlet is positioned higher. The efficiency of the compressor is 90% the material properties under usual. Let's start a solution by determining the densities. The density at the in that can easily be calculated by rearranging the idea. Gas low, the pressure, the temperature and the specific gas constant are now The density is fun 0.20 van kilograms over a cubic meter. At that, we can use this form that outlet to However, we don't know the temperature at the outlet. Therefore, we should calculate the and temperature in the next step. The ants temperature can only be calculated from the compressor efficiency. As we do not know the exact process. We only know that the idea and temperature is the temperature. Often I central week process and then we know how to connect the ideal and real and temperatures in case of ice entropic processes. We haven't recreation that connects the temperature ratio to the pressure ratio as only the and temperature of the A central big process is unknown. We can express it the idea and temperature becomes 502 cabins. This would be the end temperature. If we would neglect the losses on the compressor would have 100% official C. That is not the current case. Fortunately, we can express the known efficiency off the compressor by the help off the temperatures. Due to the loss is, there is a greater really temperature change, comfort to the idea case, the ratio off the ideal and really temperature differences equal to the efficiency. Only the rial and temperatures are the rial and temperature is 528 cabins. Now that we know this, we can finally calculate the density off the air at the outlet. Based on the idea guest. Low density equals to the quotient off the pressure and the product of the specifications constant at the temperature. The miracle they get 4.62 kilograms over cubic meter. There is just bomb task left. We must determine the shaft performance as usual. The best approach is to use the first law of thermodynamics. We need the general form off the low the compress or takes air from outside and let air out . So it is an open system. Therefore, the total Antebi change equals to the some off the shaft Work on the heat in case off compress sores. Now we use the recreation in performance units as a term for months shall be determined The compressor is insulated so that he trade is zero. Therefore, only the shaft performance appears on the right hand side the total specifications Rapid change equals to the some off the specifications up Change the change off specifications attic energy on the change off specific potential energy This is multiplied by the mass flow right To get the rate off the totally on topic change, we can substitute the known former us the specific enter big change it first the product of the iceberg specific it on the temperature change the change off specific kinetic energy egg verse to the half off. The difference off the scrap terms off outlawed. And in that velocities, the change off specific potential energy it first the product off the gravitational constant and the height difference. The potential energy change is positive. If the second state is at a higher attitude now, this is the case. If the in Latimer above the outlet, the potential energy change would be negative. We still don't know some data from the situation. The as a brick specific heat can easily be calculated by its usual formula. It's values banters and five Jewish per kilogram cabin. The mass flow rate can be expressed from the floor eight after their in that and then we can determine the velocities. The mass flow rate is the product of the flow rate and the density. It is important that both the densities and flow rates are changing, so we should either multiply Rove on and be that one or road two on reader, too. We only know the flow rate in latte, so we multiply that form. By the density of the the mass flow rate is constant according to the low of continuity. Therefore, we can only use this to calculate the venal city at the outcome of the product off density cross sectional area on Brother City are constant. To get the in lateral a city, we can divide the flow rate off in that by the cross sectional area A lot or became cat lay from the mass flow rate. Either way, the result is your appoint 139 meters per second. In case of the outlet, the mass flow rate shall be derided by the productive density on the cross sectional area. The out that speed is 0.7 to 7 meters per second. Actually, these speeds are quite small. We could nick like them in practice, but as we already know them, it doesn't hurt to calculate with them. We can just substitute into the formula and calculate the mechanical performance off the compressor or the result is photos and 52 watts. 31. Multi stage compressor – Sample problem: in practice. Usually multi stage compressor stores are used instead off single stage compressed source. In this lecture, I show you the reason why multi stage compressor sores are more advantageous, and I also show you how you can calculate in case of more than one stages. Now we keep it simple and have a two stage idea. Batting compressor air enters this compressor with Beavon pressure and Stephen Temperature the material properties off air our air and gamma. The pressure at the outlet is P four. This means the pressure off the air after exiting the second stage. The pressure ratio off the stages are the same. Some heat is released between the stages to ensure that the air enters the second stage with team on temperature. This enables us to increase the temperature Vance again. Without heat released, we would really test the durability off the compressor Materia as great pressure ratios also mean great and temperatures. This heat transfer is done in ice Obrecht manner. This is usual for heat exchangers. Finally, we note that the mess flow rate is, um that so what is the whole process for? There is an idea betting compression where no heat exchanges allowed them. He is released in ice, a barrack manner and finally there is an additional other body compression. We can split the whole process into three south processes that we can easily investigate. We must determine the shaft bear four months off the two stage compressor in the ideal reversible case. So in a charity girl case, when ice entropic state change occurs in both stages for this case, we also have to calculate the rate off the released heat between the two stages. Then we must determine the shaft pair for months in the realistic case. But we do not idealize the compressor, but instead we calculate, with the efficiencies off the stage is finally, we are going to investigate how much the shaft performance is. If the two stage compressor is substituted by a single stage ideal Adia Batic compressor that provides the same pressure ratio, the air enters the first stage at the pressure off 100 kilo Pasqua's and the temperature off 20 de Jesus is the dust description states that the are enters the second stage with the same temperature that is going to be the third state. So t three also equals to 293 cabins. The pressure at the outlet is 1600 killer Pasqua's as the state after the second compression is going to be the first state this is before the material properties are the usual ones for air. The mass flow rate is 0.1 kilograms over second. In the irreversible case, the efficiency off the first stage is 60% on the efficiency of the second stage is 70%. In the first step, we are going to determine the properties off every process. We need the pressure and temperature at each state. Let's start by calculating the pressures the inlet and outlet pressures are known. We only need to determine the pressure after the first compression and before the second compression, we can calculate the total pressure issue. It means the ratio off the outlet and being left pressure. The New America is out of 16. There is an ISA Barak heat transfer between the two compressions. So the and pressure off the first compression it first to the initial pressure off the second compression. We only have to calculate one missing pressure later. It is enough to derive the pressure issue off the individual stages. According to the dust exception, the brash ratio of the two stages is the same. Therefore, the resultant pressure ratio equals to the squared off the pressure ratio off one stage. The resultant pressure ratio is always the product off the separate pressure ratios. If the pressure issue of the stages is the same, the poverty appears now. The pressure ratio off one stage is the square root of the total pressure ratio. Either P two over Trayvon or P four over Petri egg. First of four. If we want, we can calculate B two that equals two b three, but we do not really need that. We just need the pressure ratio, which which we can calculate the necessary temperatures. We need the and temperatures off both stages. The compression is Adia Batic, and in the first part of the problem, the compression is also reversible, so we can calculate with a central, picky creations. The temperature ratio can be expressed by the half off. The pressure ratio and Adia Batic exponent, be to over people on the first of the pressure ratio off one state, so we can just substitute that instead of the pressures. Furthermore, the same pressure ratio is valid for the second stage. Do that for P For over. BT also requested happy stage by using the ice entropic equation. For the second compression, we finally get that t four over t three equals T two over TV from a Steven anti three. The initial temperatures are the same and temperatures are also the same. T two and t for expert to 435 cabins. If Stephen anti three are not equal, you could calculate and temperatures separately, but with the same kind of figuration. Now we know the necessary temperatures and pressures we can calculate anything for. The isn't every case. We can concentrate on determining the performance off the compressor. As usual, we can use the first load off thermodynamics to calculate the perform. Us. There are ice entropic processes in both stages. That means that the heat rate is zero. The rate off the total anti P equals to the shaft performers, which means the mechanical input performance of the compressor. The anti operate can be calculated separately for the two compressions. The product off the mass flow raid ISA very specific. It and the temperature changes taken. Actually, we must calculate with the third process to however, the shaft work or shaft performance is euro in case of isil, Barrick processes. So the performance is euro for the as a brick heat rallies. That's why it is not in this formula. The answer. Brake specific. It eat first, the 1005 she was over kilogram cabin based on the usual. For now, we know everything. We can calculate the performance in the idea reversible case, the necessary performance to operate the compress or equals to 28.5 kilowatts between the two compressions stages. He is released from the system and we were asked to calculate the rate of this released heat. There is an ISA Berkey through these. As I mentioned earlier, the sharp work off this person's zero that for the first law of thermodynamics only contains the heat and the Antara P. In case of this open system, the he trade equals to the ant operate as usual, the inter operate equals the product of mass flow rate, the iceberg specific it and the temperature change which shall be calculated between the third and second states, 14.3 kilowatts is the heat rate. The negative sign indicates that this heat is really taken away from the system. The correct answer for the question is that the rate off the released heat is 14.3 kilowatts foreign 0.3 kilos. Your heat is extracted from the system in every second. Now we can calculate the bat for months off the irreversible case. The pressure ratios are the same, but the temperature ratios change. There's an irreversible process in both stages, but the processes are still a diabetic, so there is no heat transfer during compressions. Also, there is no shaft work during the ice break eateries. The performers can purely be calculated. Based on the compressions. We can use the definition off the compression official C to connect the previously calculated idea case to the current realistic case. The ratio of the ideal Andrea performance is equal to the efficiency. Therefore, we get the real performance. If we divide the idea performance by the efficiency in case of a compressor, the invest energy into the system. If the process is not ideal, we need more energy. That's why Sharia performance is greater than the idea of, um, you can just make this creation up by thinking of these relations. I only talk more about this at the relation is the opposite for turbines. In case of turbines, we get energy from the system. In an idea case, we get all of the available energy. But in realistic case, we get less energy from a turbine. Therefore, the rial performance. If a turban is smaller than the idea there for months, if we had to calculate the same measures now, we would have to multiply with officials instead of dividing it. If we would work with the turbine anyways, just think of the basic relationships. Now. The numerical results is 44.2 kilowatts. Actually, you can calculate in a slightly different way, too. De Tu minus Stephen and T four Manistee. Dreaming the ideal temperature differences from thes and efficiencies, you can calculate the rial temperature differences with which you can calculate the performance. Finally, let's check out the last case. This time we substitute the two stage compressor with the single stage compressor by ensuring that the total pressure ratio stays the same for simplicity. Now we are going to calculate with an ice intra big process just as the task description told us to do. The total pressure ratio is the same as before, but there is only one compression. This contraction is eyes entropic, so the temperature can be calculated by the usual ice entropy creation. The temperature ratio can be calculated by the help of fresh aeration of the abutting exponent on the and temperature becomes 647 cabins. This temperature is higher than the and temperature of the two stage compressor. As no heat is released, Let me mention that this has a practical relationship that you should consider the single stage compressor could have. A temperature with which the materials of the compressors get ruined mean by the multistage compressor has lower temperatures where new problems arise. The shaft performance formula has already being used. The performance it was until operate, and now we substitute the initial on temperatures off the compression 35.6 kilowatts is needed to reach the required pressure ratio. Let's compare this to the earlier result. The two stage compressor only requires 28.5 kilowatts to get the same pressure issue by not having to increase the temperature so high that there for months. Need is also getting smaller. This is my Morty stage compressors Adverse spread in practice. Even if the motive stage compressed source are more expensive to be on, the operation is cheaper. Not only smaller performance is enough to run the compressor. We could also make use off the released heat or so without changing the materials and the quality of the compressors. We can increase the outward pressure by using more diverse stages. We are not restricted by the durability off compressor materials in this case or not the restricted that much. 32. Carnot cycle: The carnal cycle is important in theory, as it has the highest possible efficiency off all cycles. Forgive a minimal on maximum temperature limits. The kind of cycle consists of four steps and off course. The start and the end state is the same as it is a cycle. Now I tell you how you can do work with the half of the carnot cycle. In this way, you can use the car not cycle as a power cycle in the heat engine. If you change the direction off the processes, the candle cycle would work as a heat pump or a cooling machine. First, the cycle starts with an acid thermal expansion between 0.1 and two. In practice, this means that he transfer with a he tanked, during which the medium receives heat from the heat tank and the medium expands. This heat tank is a source after that comes and ice entropic expansion from point to 0.0.3 . So we insulate the medium and we expanded without any heat transfer or losses. So in this stop, the medium purely does work. From 0.32 point four, we go to a NASA timer compression, so there is a gun. He transfer between the medium and the heat Tunc. But this time the medium gives heat to heat tank by its volume decreases. This heat tank is a sink. Finally, a nice entropy. Compression completes the cycle. We arrive back to 0.1 from point for In this step, the system is insulated. There is no heat transfer. We purely do work on the medium to compress it to the starting For you, the operation off the cycle is going to be more clear to you. After we take a close look on the diagrams on the PV diagram, you can see how the volume is increased in the 1st 2 stops. At the first step, the volume is increased in an ice, a term, a manner then from 20.223 the volume is further increased in I central big manner. Then there is a compression from 0.3 back 2.1 first at an ice attire. My manner done at an ice entropic mother. On the ts diagram, you can easily see the type of processes the horizontal lines are isa terms. The Vatican lines are ice and probes. So after seeing the processes but can you also see on the TV diagram? The closed area equals to the work done by the medium during the cycle On the TS diagram, the closed area is the heat transfer to the medium. This is how the candle cycle works as a heat engine. If you want to operate it as a heat pump, you only need to reverse. The process is so just imagine that you have to take the opposite. Directions on the arrows are reversed. In that case, the medium does not receive the heat. He quoted a closed area and that yes diagram. But the medium gives that much he to the environment while work is done on the medium. Previously, I defend the terminal efficiency, which can also be calculated for the kind of cycle the formula can be re Britain. And it is easy to see that the maximum possible efficiency can only be reached by minimalize ing. The heat output and maximal izing the heat input in case of the candle cycle. This can also be river eaten with temperatures as the heat transfer is ISA terminal in boost directions. Suppose the heat supply and the heat rejection is ISA turmoil. The efficiency becomes greater by decreasing the temperature off the heat rejection on increasing the temperature off the heat supply. Forgive a maximum and minimum temperatures. The kind of cycle has the best efficiency. If any of the points of the upper line goes lower, the supplied heat becomes less, which decreases efficiency or so. If any point of the bottom line goes up for the heat, rejection will be greater, which also decreases the efficiency. You must remember that the candle cycle is the Optima, but off course theoretical solution. It is not possible to do this perfect, Aiko. 33. Equivalent Carnot cycle: it is pretty easy to handle the camel cycle, and it is especially easy to calculate its efficiency. That is why the active aunt can off cycle is introduced, which is used for analyzes in case of complex processes. Some of these complex cycles would be very hard to handle, but by substituting it with the colonel cycle began the of it down. Let's take an arbitrary cycle just like the one that you can see on the left hand side. The process from Point want to point to miss heat addition to the system done from point to the 0.1, there's heat rejection from the system. This cycle can be substituted by an act prevalent candle cycle. There is also heat addition on rejection in the can off cycle, but these are ISA term our processes to do the substitution. The average temperature off the heat addition and his rejection can be calculated. These average temperatures rt in and t out. On the right hand side, you can see a candle cycle that is operating between the same entropy limits, but with Isa termer heat exchange. By the definition off the average temperatures, we can ensure that the work output is the same for the two cycles that you can see here. Remember that this work output is the area off the closed space, which is also the difference off the heat. Addition and heat rejection. Let's define the average temperatures. The average temperature off the heat supply or heat addition is the average off the integral off the temperature function. With respect to the entropy, the average temperature off the heat rejection is defined in the same way. It is also the average off the integral off the temperature function with respect to the entropy. So basically, only the usual average off the temperature is taken. I have already told you about the turmoil efficiency off the can off cycle after substitution. The efficiency off any cycle can be calculated by the half off the average temperature of the heat. Addition and heat rejection. The maximum off the efficiency can be defined by half off the temperature maximum and minimum off the original cycle. The efficiency would be the best if in the origin cycle the heat addition would happen or the way at the maximum temperature on the heat, rejection would happen on the temperature minimum the closer we get to the shape of a candle cycle, the higher the officials is. Also, if we can push the temperature maximum higher on the temperature minimum lower, the efficiency is greater. The shape of the function can be perfect. ID until a certain degree by modifying the processes in case off the temperature limits. The upper limit is critical. It has some technological limits. The matter areas can only withstand a certain temperature. For the lower limit, we can usually use the ambient temperature. The temperature can barely be decreased from the normal atmospheric temperature. 34. Equivalent Carnot cycle – Sample problem: let me show you a sample problem to practice the calculations related to the Akron kind of cycles on the terminal efficiency. The terminal efficiency off a power cycle is given the specific rejected heat or so could specific heat output is also given the mass flow rate of the medium inside the cycle is on dirt the average temperature of the heat Rejection ISTEA out. We must determine the useful performance off the power cycle, the heat performance input or heat supply on. We must determine the average temperature off the heat supply. The data are the following. The Tamil efficiency is 75%. The specifications output is 500 kilos juice per kilogram. The mass flow rate is 10 kilograms per second and the average temperature of heat output is 25 degrees C, as is or 298 cabins. Let's start the calculations with the heat performance input as it is needed for determining the useful performance. The formula for the timer efficiency is known. The terminal efficiency is one minus the ratio off the heat performance output on the input . This is the ratio of hit supply and rejection in power dimension as the terminal efficiency is known, this is a good starting point. The specific heat output is known from which the heat performance output can be calculated . The heat performance output is the product of the specific IT output and the mass flow rate , which years to 5000 kilowatts. The heat performance input can be calculated now by rearranging the form love for the Tamil efficiency. The heat performance output must be divided by from minus the thermal efficiency. The result is 20,000 kilowatts or 20 megawatts. Now we know everything to calculate the useful performance. It is the product of the Tamil efficiency on the heat performance input. This formula is valid because the efficiency is the ratio of the useful quantity and the total input quantity, and now the work or the related performance is useful in the power cycle and the heat supply or the heat. Performance input is the total input quantity. The result is 15 megawatts or we need now is to calculate the average temperature of the heat supply. Again, it is voted to go back to the terminal efficiency in case of the equivalent carnal cycle. The Tamela efficiency is calculated by the help of the average temperatures, this formula can be rearranged to get the average temperature off the heat supply. Everything else is known, so we can substitute. The result is 1192 cabins or 919 degrees Ozzie's. It is a quite high temperature, so you can see that great efficiency requires high input temperatures. 35. Otto cycle: the auto cycle is an idealized cycle. It describes how a spark ignition pieced on engine operates, usually as notes of the cars have internal combustion engines working according to the auto cycle. You see the application of this topic every day. The indicator diagram off the cycle can be seen on the figure. The indicator diagram is easily determined by measurements with a device that measures the pressure as a function of the volume. The auto cycle is a four stroke cycle, so the volume changes in these four strokes between the minimal and maximal value. The whole process happens inside the cylinder, and the volume is changed by the half off a pistol. But the space is not closed. There is material intake and exhaust. First of all, there is an intake between Point A and B. A mixture of air and fuel is taken in from an environment with atmospheric pressure. During the in, take the pressure off the mixture drops below atmospheric pressure due to the losses. This is the first stroke. In the second stroke, the gas align air mixture is compressed. This is done until reaching point C. At the minimal volume, we must always take care to not reach the outer ignition temperature during the compression . In case of ultra ignition, the mixture starts burning, which is harmful for the auto engine. At this point, if the ignition happens in the stroke, you can hear Jaring from the engine. In case of the auto cycle, there's always a controlled ignition. The mixture should only start burning because of the ignition at Point C. The combustion happens between Point C and the. As the mixture burns pretty quickly, the process has almost constant for you. The third stroke comes after this. The burn fuel is expanded from Point B to Point E. Then the excess 12 opens, which leads to a quick blow down between Point E and off. As this is also a quick process, the volume is basically constant. In the fourth stroke, the remaining flue gases exhausted as the peacetime pushes it out of the cylinder. After this, the cycle starts over. We could calculate with this indicator diagram, but rather use an active on cycle that only contents idealized state changes. We can calculate more easily with that, and the motorcycle is the equivalent cycle. Actually, the esoteric processes are easy to recognize from the PV diagram. The other processes can be approximated by ice entropic processes to create an Akron cycle . We need simplifications as it is not easy to calculate with an open system, but also chemical changes are happening during combustion. The first assumption, according to this, says that there is no chemical change instead of that external heat exchanger is used. So the heat addition off the combustion is model. With a NASA cricket exchange, we assume I sent a big expansion and compression, so we assume that there is no heat exchange during the expansion and compression. So they are idea Batic or so it means that there is no loss. So these two processes are reversible. The blow down and exhaust are also substituted by an external heat exchanger. So we calculate with an icicle Rick heat rejection. Finally, the effect of intake is assumed to be negligible. We do not calculate with the losses that happened during intake. To sum up, we have a close cycle which has to a central pick on to as a creek state changes. Let's take a look at the actual violent cycle in a PV diagram from the starting point. There's an eye Centobie compression to point to. The step requires Burke input to the system done on isil. Correct. Heated Isha happens between 0.2 and three, which increases the energy off the system between state three and four. The engine does work by using the previously increased energy. The work is done during an ice entra big expansion. Finally, on Isa Couric state change takes us back to the starting point. The exact same happens on the TS diagram. There's an ice entropy compression on the ice, a Keurig heat addition to increase the energy level of the system. The work is done between state three and four from this energy on. Finally, the remaining heat is rejected from the system. To get back to the starting state for calculations, you can always use the formulas that you have learned for each specials they change and also the other previously learned formulas. The motorcycle means a close system as it is the equivalent cycle off the Rio cycle. In the close system, the change of internal energy equals the sum off heat on work as the heat exchange on the work belong to different steps they're independent and the formulas are even simpler During heat addition, there is no work, so the heat addition between state to entry equals to the change of internal energy between those states. That means that the product of the Isakovic specific heat and the temperature change is the heat input. Similarly, the heat rejection is between states for and fun. Be careful about the signs. The heat rejection is considered to be negative as it takes energy away from the system by the concentrate to be positive only if it increases the internal energy. So the heat rejection is minus von times the change of internal energy, which gives us a formula similar to the pre orphaned. But be careful with the role of the temperatures. Based on the ice entropic expansion and compression, the temperature ratio can be deducted. According to that, the ratio of the first and second or the forced on third states temperatures equal to the ratio of the second and first states volumes to the father of gamma minus one. We can define the compression ratio as the ratio of the volume maximum and minimum it eek first to weave on over V two This is an important quantity in case of an auto cycle. For example, the thermal efficiency can be expressed with the help of the compression ratio. According to the formula, the terminal efficiency increases if the compression ratio increases. It is important to note that the compression ratio can be increased by much as we need to avoid outer ignition. In practice, the compression ratio is between seven and 11 or so. The greater the Adia Batic exponent, the greater the efficiencies. But there are only a few choices for material, as it also needs to be able to burn felt in the combustion. 36. Otto cycle – Sample problem: after getting to know the auto cycle, it stand to see a sample problem to practice. Ideal low to cycle is investigated. The medium is at P, even pressure and even temperature before compression at the bottom that center of the piston. The volume is women. The compression ratio is RV, the highest temperature, and the cycle ISTEA marks. The medium is an idea gas. The specified gas constant is. Are the Adia Batic Expand is come. We must determine the heat. Addition, the useful work, the thermal efficiency of cycle on the mean, effective pressure off the cycle. The data are the following in the first state. The pressure is 100 Kill a Pasqua's. The temperature is 293 cabins. The minimum value off the volume is 100 cubic chancing meters. The compression ratio istan. The maximum value off the temperature is 2000 cabins. The specific gas constant is 287 shoes back kilogram cabin. The idea Batic expand is one point for first, let's look at the actual in cycle and check what we do know and what we need to determine. I have done the numbering in a way to ensure that state number of on is the state before compression. After the complexion, we are in state number two. The volume equals the minimum volume. At this stage and also in the stirred state. The maximum temperature occurs at 0.3 after the Isar correct heat addition, so we know the temperature at ST number three. One of the questions is the heat at the Shem between state number two country to calculate that we are going to need the temperature off state number two. The next step is an ice entropic expansion during which the medium does work. The useful work equals the difference off this work and the work input during the ice entropy compression From State number four. There's an ISA cricket rejection to state Number fund. We could also use this on the heat addition to calculate the useful work. Let's start the calculations with the heat addition. As I showed you in the previous lecture. The heat addition can be expressed by the change of internal energy between state number two entry as there is an ISA correct process in a closed system. In this formula, we only know the temperature off state number three as it equals to the highest temperature value. State number two is right after the ice entropy compression, which has known starting temperature. The temperature after the compaction can be determined by the half of the formula. Describing the ice entropy compression. The best way of solution is to express the temperature ratio by the half of the compression ratio. By rearranging the formula, T two equals the product of Stephen and compression ratio to the power of gamma minus one. It is 736 Gavin's. We still need a couple of perimeters to calculate the heat Addition the mast cam of written by the help of the idea gas low in any of the states. I used state number one as we know almost everything. At that point, we only don't know the volume, but that can be calculated as the product of the volume at ST number two under compression ratio, this formula is valid because state number two has the lowest volume and state number one has the highest volume. During the 02 cycle, the must becomes 1.19 times 10 to the power off minus three kilograms. The isakovic specific it can be expressed with the other material properties. It is our over gamma minus one, so it is 718 Jews per kilogram cabin. Now. The heat addition can be calculated as everything is known in the formula. The result is 1079 Scheuer's. I determine the useful work by the half off the input and output heat. The heat rejection can be calculated by the help of the temperatures at ST number four unfunded. So we need to determine the temperature at ST Number four, which is right after the expansion. Its temperature can be calculated by using the formula for the ice entropic state change, just like we did. In case of the compression, the temperature off state number four can be calculated by the half off the temperature Estate number three on the compression ratio. Be careful with this is, but basically we use the same formulas before the result is 796 covers. Now we can calculate the heat rejection, which is minus vantage. The heat transfer between states number four and fun as the expression Heat rejection already indicates minus side as heat rejection is always a negative. Heat transfer the heat transfer equals the change off the Internet energy. The formula is similar to the van in case of the heat. Addition, the product off the Mass Isaka expensive ticket on the change off temperature is taken now , the temperature off the latter status subtracted to get the proper sign. The result is 400 turned visuals, which actually means negative heat transfer with an absolute value off 400 card issuers. The useful work is the difference off the input and output heat transfer. Most of them are known, so we get the result, which is 649 Scheuer's. We got this formula from the fact that the resultant heat in good can be used to make the cycle do useful work. The rest of the questions can be answered by phone on one formula. The town of efficiency is the ratio of the useful work on the input heat, or so could heat addition. In case of the auto cycle, you can also calculate with the help of the compression ratio, the result is the same for both formulas. The Tamela efficiency is 60.1%. The mean effective pressure is the ratio off the useful work and the difference of the volume maximum and minimum, the volume maximum can be expressed with the minimum on the compression ratio. The mean effective pressure is 720 avuncular Pasqua's. 37. Atkinson cycle – Sample problem: The Atkinson cycle is also used in internal combustion engines. Basically, it is a slight modification off the auto cycle. In the problem on ideal, Atkins, or cycle is investigated. The cycle is similar to the auto cycle, but the heat rejection is Isa barrack before the compression. The pressure is P one, and the temperature is Stephen. The compression ratio is RV. During the other cricket addition, coup in hit is transmitted to the medium. The medium is an idea. I guess it's specific gas. Constant is are the idea. Batic exponent is Kama. He was determined the specific useful work, the thermal efficiency and the mean effective pressure. The starting pressure is 100 killer Pasqua's The temperature is 300 cabins. The compression ratio is stand. The specific eat input is 1500 kilo, she whispered. Kilogram. The specific gas constant is 287. She was back kilogram cabin. The idea Partick Exponent is one point for Let's take a look at the Atkins all cycle. You can throw it diagram by only using the data in the program description. Similarly, to the 02 cycle, there's an ice entropy compression on Isaac Rick Heat addition. And then I center big expansion. The difference is that the heat rejection is not ISA correct, but I said Barrick now. Therefore, the expansion is done until a greater volume, which increases the amount off useful work. Basically, we have to go around the diagram step by step, to answer each question. We can start with the I Centobie compression, as its starting state is now to get the pressure. After the compression, you can express the pressure ratio by the compression ratio according to the formula off the ice enter big processes. The volumes are unknown, but we can calculate the pressure at ST Number two as we know the compression ratio. The pressure at ST Number two is 2512. Kill A Pasqua's. The temperature after the compression can also be expressed by the help of the compression ratio, but you can also use the idea of gas low. The temperature off State number two is 754 cabins. There is as a cricket addition in the next step. The specific eat addition can be calculated based on the first love time of dynamics as the external work zero in case of isil correct processes. So we only need to calculate with the change of internal energy the esoteric specific. It is unknown, but it can be determined by using the other material properties. The icicle expensive ticket becomes 718 you a packet program cabin. In the end, temperature off the heat addition can be expressed from the heat addition. It becomes 2843 cabins. The pressure after the compression can also be calculated in case of Isaac. Correct process is the ratio of temperatures, and pressures are constant. We can use it and get the pressure at ST Number. Tree is 9470 to kill Oppa scowls. The next step is the isn't tripping expansion. The pressure after the expansion is known as the next process is an Isa Berrick heat rejection. So the pressure at ST number four equals to the pressure off state number of on. So it is 100 kill a pass cars. The temperature after the expansion can be calculated by the formula off the A central big processes. The ratio off temperatures and the ratio of pressures are in a known relation to each other . From that, we can calculate the unknown temperature. It becomes 775 cabins after knowing the end points off every process. The other calculations are simple. We still need one perimeter as a brake specific heat. The acid very expensive ticket is the product of the Isakovic specific it and Adia Batic exponent. It becomes Montas and five shoes Party program cabin. The specific heat rejection can be calculated now. It is the absolute value off the change of anti RB during the eyes. Bereket rejection. That's why there is a negative sign in the formula. The product off the iceberg specific heat on the change of temperature leads to a specific heat rejection off 447 kilos. US par kilogram. The specific useful work is the difference off the specific input and output heads. So it is 1023 kill Oshawa Spar Kilogram. The Tamela efficiency is the ratio off the specific useful work and the specific input heat . It is 68.2%. In the present case, the mean effective pressure is the ratio off the specific useful work on the total change of specific volume. Therefore, the difference off the maximum and minimum of the specific volume mistaken. The maximum means we for the minimum is V two. They are not known yet, but we can use the idea gas low to obtain them. The specific volumes equal to the product of the specific gas constant and absolute temperature over the pressure. In state number two, it means 861 10,000 cubic meters per kilogram. In ST number four, it means to 40.22 cubic meters. Macular Graham. By substituting back, we get that the mean effective pressure is 479 Kila Pasqua's. 38. Diesel cycle: the desire cycle is a combustion process off reciprocating internal combustion engine. It is vast spread because of its good efficiency compared to the auto cycle. The main difference is that in these air cycle, the ignition is done. But he generated during the compression off air. Let's in details how these an engine works. The indicator diagram off the four strokes process can be seen on the figure similar to the auto cycle. The processes take place in a cylinder close by a piston, but there is material in and outflow in the first stroke intake happens during which fresh air is taken in at atmospheric pressure. This pressure drops due to the losses. That's what you can see between points A and B. In the second stroke, this fresh air is compressed between Point B and C. As there is no fuel, the temperature can be increased way further than in case off the auto engines. This high temperature is needed as there is no spark ignition in the diesel engine. Instead of that, the high temperature off the compression is enough to immediately ignite the fuel injected at the third stroke. Therefore, the combustion happens during the injection, which leads to a basically constant pressure after the end of the combustion. The third stroke ends with an expansion between Point D and E, then the access to have opens, which leads to a creek blow down between Point E and F at an almost going stand for you in the forced stroke. The remaining flue gas is exhausted by the piston from the combustion chamber. You can see that the desire cycle is quite similar to the auto cycle. It is important that fresh air is taken in by in case of the auto cycle fuel air mixture rece taken in. The other difference is the ignition, as it is done by the high and temperature of the compression during the injection in case off a diesel cycle. But it is done with this park in case, often auto cycle. Therefore, the combustion is Isa Barrick in case of diesel engines and Isaac Orrick in case of auto engines. Besides these differences, we can use the same assumptions inactive alone. Psycho can be made based on the assumptions. Let's check it out in a PV diagram from the input, there is an ice entropy compression to the second state. This step needs extent of work Input done on isometric heat Addition happens with me states to entry. This heat addition increases the internal energy of the system. Then work is done by engine during an ice entropic expansion. Finally, on as a creek state change brings the system back to its starting state. The same can be seen on the TS diagram after the ice entropy compression. The heat is supplied to the system during a nice Abric. Heat addition discovers the energy need off the work that the engine can do during the eyes . Entropic expansion between 0.3 and four. Finally, the remaining heat is rejected from the system between 0.4 and fun from point to the diesel cycle goes on with an ice abric state change. But I indicated the Isaac or going to death point the auto cycle would use that line as its heat addition is Eissa Couric. Obviously, the area under the curve would be greater in that case, So why do we use the diesel psycho? It is because of the greater compression ratio with which higher temperature can be reached . So actually the temperature of 0.2 is much greater for these a cycle compared to an auto cycle. Therefore, in fact, the upper line off the DEA's A cycle goes higher, which years the more useful work on better efficiency formulas can be directed to calculate . You can always start from the first law of thermodynamics. The equivalent cycm is a closed system so that four must be used during the heat addition between point to one tree. There is also work. Therefore, the heat addition equals to the difference off the change of internal energy and the work. The extent of work often Isa Berrick State change can easily be calculated by the product off the constant pressure on the change of volume. It can be noticed that this expression it first the change of anti happy. Therefore, the heat addition equals to the product off the iceberg, specific it and the change of temperatures according to the definition Off the eyes uber expensive ticket. It is quite obvious to calculate in this way during the heat rejection, there is no work, but you must be careful to use the proper sign. According to the terminology, this means that the heat rejection equals two minus one times the heat supply to the system between 10.4 and fun. You can calculate the product of the icicle expensive ticket and the absolute value off the change of temperature, which is t four minus t one. The temperature ratio can be deducted. It is important to note that only the ratio of the temperature off state number one and two can be calculated like this. The ratio off the temperatures off state number three and four can be calculated analogue loosely with their own specific volumes. The compression ratio has already been defined in case of the auto cycles. It is the ratio of the volume maximum and minimum. The cut off ratio is the ratio of the volumes off state number three and two. These are the limit volumes of the combustion face, so the cut off ratio characterizes the volume change during heat. Addition, the terminal efficiency can be expressed by using the compression and cut off ratios. The formula is similar to the formal of the auto cycle. The difference is the term in the brackets. The smaller the cut off ratio is, the higher the efficiencies. The maximum occurs when the cut off ratio is one which actually relates back to the auto cycle. Despite that, the efficiency of these are engines our creator. As the compression ratio is greater than in case of auto cycles. In case often Oto agin, the compression ratio is usually between seven and 11 but in case of the diesel engine, the compression ratio is approximately between 15 and planetary. 39. Diesel cycle – Sample problem: let me show you a sample problem related to these are cycles. This is going to help you understand. Memorized the diesel cycle, an idea these air cycle is investigated. The medium is an idea. Gas. The specific gas constant is our. The pressure and temperature is given at the ends off the state changes the ice entropy. Compression starts a safe one, so the numbering is done accordingly. We must determine the compression ratio, the cut off ratio, the specific eat addition, the temporal efficiency and the mean effective pressure before the ice entropy. Compression. The pressure is 100 kilo Pasqua's and the temperature is 300 cabins. After the compression, the pressure. It's 5000 killer Pasqua's and the temperature is 900 cabins in ST Number Tree After the Isil Bereket addition, the pressure is still 5000 killer Pasqua's. The temperature increases the 1600 cabins after the ice entropic expansion. The pressure is 200 killer Pasqua's The temperature is 600 cabins. The specifications constant is 287 Jewess back kilogram Kavin. Let's take a look at the active aunt cycle. The pressure and temperature off each main points are given, and the state changes are the polluted idea. State changes there is as entropy, compression between point violent to then comes and ice berry heat. Addition. A nice entropy expansion. Andan isa Cricket Rejection. This eh Cuban cycle of the diesel engine is a master no for calculations as the form last camp of written quite simply, according to the diagram, let's determine the material properties first as we are going to need them, but only the specific gas constant is given. We need to know one more, and then we can use the creations among the material perimeters. The idea batting exponent can be determined based on any off the ice. Enter big stay changes. Now I use the formula between the temperature ratio and the pressure ratio in case of the ice entropy compression. This formula is ready to know, but it can also be deducted from the idea. Gas low on the basic equation off the ice entropic state changes they made from the rule p times we to the power of gametes constant. That's express gum. Gamma is the recipe broker off the terms in the bracket. The local rhythm off the equation must be taken, the expanse can be brought in front of the logarithms, and then you can rearrange everything. Goma is 1.39 which seems to be right, as the idea, Batic explained, is usually around 1.4. The icicle expensive ticket can be calculated as our over gamma minus one, which means 736 Jewess Back kilogram cabin, the as a brick specific. It is gone more times the ice, a Keurig specific it. So it becomes 1023 juice bar kilogram cabin. You just need to remember the two violent excavations among the battery of properties, and you can be like the formulas I used here, some off. The results can be determined instantly. The compression ratio is the ratio of the volume maximum and minimum. With the current numbering it is, we won over V two. The volumes are unknown, but the ratio can be expressed by the half off. The pressures the quantities present in the A creation are well connected through an ascent , a big state change because of the ice entropy compression even times we want to the partner of comma. The 1st 2 p two times v to the power of Kama, which year it's to the equation that you can see here. The compression ratio becomes 16.7. The cut off ratio is the ratio of the volumes of the and states of the ISA Barrack ST Change. These volumes are unknown, but the ratio can be expressed by the temperature ratio during an iceberg state change the ratio of the volume and the temperature remains constant. From that, the cut off ratio is expressed a sti three over t two. The result is 1.78. The specific heat addition happens during an ice brick state change between state number two and three. We work in a closed system, but as there is some work done by the system, we get that the specific E tradition equals to the change of specific Antara p between the two states. So we need to calculate the product off the as uber expensive ticket on the temperature change which years 716 kilo Chua sparking program. As a result to calculate the Tamela efficiency, the useful work is needed for that. Either all of the works are needed or we can use the heat in the second case, we only need the heat rejection as a further data. The specific eat rejection belongs to the ice and CORIC state change. The afford specific IT rejection equals to the change of specific internal energy. According to the first love, the AM Madonna mix. For this closed system, this is only true as the external working zero in ice a career case. The negative sign is only needed because of the terminology, as a positive amount of heat is rejected altogether, its effect is negative for the system. The product of the icicle expensive ticket on the temperature change between state number four and one results in 220 van kill Arduous bar kilogram specific teacher shampoo. The use with specific work is the difference off the input and output hits, which means 495 kill Oshawa, sparking program. The terminal efficiency is the ratio off the use with specific work and the specific eat addition. The efficiency it becomes 69.1 person. The mean effective pressure is interpreted as the pressure with which the volume change would need to be multiplied together. Useful work as we do not know any of the extensive state bribers. We've tried the formula with specific state where I a bus. The mean effective pressure equals to the ratio off the useful specific work on the change of specific volume. The change of specific volume is taken between the and positions off the piston. The specific volume off State number two can be written by the ratio off the specific volume off state number of fun and the compression ratio. We still need to obtain the specific volume at ST Number Fun. It can be determined from the idea of gas slow. The specific volume equals to the product off the specifications constant and absolute temperature over the pressure. In the present case, we got 0.861 cubic meter sparking program. By substituting into the formula, both the mean effective pressure becomes 600 perfect Pasqua's 40. Sabathé mixed cycle – Sample problem: the somebody mixed cycle is a terroristic, a cycle that is the mixture off the auto, and these are cycles. In reality, the processes are somewhat more similar to the Sabbath cycle. An idea somebody cycle is investigated before the compression. The pressure ISP even, and the temperature is Stephen. The compression ratio is RV. The and pressure off the as a cricket addition is Petri. During the Asbury combustion, the volume increases the 1.5 times it's starting value. The medium is an idea, I guess. The specified gas constant is. Are the Adia Batic exponent is Kama. The mass flow rate is am dot We must determine the useful performance and the terminal efficiency off the cycle. At the intake, the pressure of the air is 100 killer Paschal's and its temperature is 300 cabins. The compression ratio is 15. The and pressure of the esoteric combustion is 50. Bar, which is equivalent to 5000 kill a Pasqua's the and volume off the Asbury combustion is 1.5 times it's starting value, so we four equals to 1.5 times Vetri. The specific guest constant is 287 she whispered. kilogram cabin. The Adia Batic exponent is one point for the mass flow rate is Van kilogram per second? Let's take a look at the Sabathia cycle. There is an ice entropy compression in the first step. Then the heat addition is done in two steps. First in ice, a correct manner between 20.2 and three on. Then in Isa Barak manner, Auntie a point for an ice center pick expansion takes the medium to state number five. Finally, on either bury, heat rejection closes the cycle. Technically, the somebody cycle is almost the same as the photo, and these are cycles. Only. The heat addition differs in case of the cycles, as in reality, it is more likely that the shape of the diagram looks like the diagram off the Sabbath day cycle. Instead of the other two idealized psychos. Let's go through the state changes. First. There is a nice entropy compression you can use the formulas valid for as entropic state changes. The pressure after the compression is the product off the initial pressure on the compression ratio to the power of gum. It means 4403rd avuncular bus cars, the temperature after the compression can be expressed by the compression ratio or by the help of the idea. Gas slow. Its value is 886 cabins. The heat addition is done in two steps. The and temperature off the esoteric heat Addition can be calculated as the protect off its initial temperature on the ratio of the pressures in case off Isaac Oryx, they changes the ratio off the temperature, and the pressure is constant during the horse they change. That is why we could calculate like this. The result is 1000 Gavin's in case of the isil backs. They changed the ratio off. The temperature on the volume is constant, therefore the and temperature off the ISA Barrick he tradition is the product off its initial temperature and the ratio of the volumes. The result is wonders and 500 cabins. Let's calculate the heat addition. For that, we are going to need the matter area perimeters. The massacre expensive ticket is calculated in the usual manner. It is 718 Jewish back kilogram Kavin, the Assab Eric Specific. It is gonna times the Isa Coric one. It is 1005 shoes per kilogram cabin. The heat addition is done in two steps. In the 1st 1 there is an ISA Cukaricki tradition that can be calculated as the product off the Isakovic specifications and the change of temperature in the second step, the ice Obrycki's tradition is the product off the as a brick specific it and the change of temperature. The some of these leads to 584 kill Oshawa Sparkler Graham. That is the total specific eat addition. The next step is a nice entropic expansion. The and temperature off the expansion can be expressed by either with the ratio off the pressures or with the ratio of volumes Neither of them is known. Yet The ratio of the volumes is the one that you can determine more easily. The volume is the same in state number 500 is there is a NASA correct state change between them. William Number four is 1.5 times volume number tree. According to the problem description. The volume off state number tree on to equal to each other because of the other correct state change V two over everyone equals to the reciprocal off the compression ratio, which is known after a substitution. The temperature after the expansion becomes 597 cabins. The useful path four months can almost be calculated. Only the specifications rejection is needed, which can be calculated as an answer. Correct state change between state number 500 on the specific IT rejection is the product of the other Keurig. Specific it on the change of temperature. Be careful with the size. The result is 213 kilos. Chua Sparking program The useful specific work is the difference off the input and output heat, which means 370 van kilos US parking program. This must be multiplied with the mass flow rate together. Useful performance. It is 370 Vonk. You know what the terminal efficiency is? The ratio of the useful specific work on the specific it addition Numerical E becomes 63.5% . 41. Brayton (Joule) cycle: guess turbans work according to the breakdown cycle. It is also called you Cycle or celebrate on Psycho. As it is the working principle off gas turbines. It is the third very important cycle besides the auto cycle on these are psycho. Let me show you the idea of great on cycle. You can see it in the PV diagram. Similarly to the other cycles. We use a closed system in the equivalent cycle, even though the system is open in reality, in case of the Brayton cycle, it is not very far from reality to consider that the system is closed. It is actually open to the alibi amount. But the end state is the same as the starting state. So the cycle is closed through the environment. Let me get you through the state changes and you will see the sense in the statement. First air enters a compressor where it goes to a nice entropy. Compression between states Want to hear the fuel is added to the system and it is burned. Is that off? Considering burning, we use a heat exchanger in the model. According to that, there is an as a barrack heated issue between state number two entry in the heat exchanger , the pressure remains constant While heat is supplied to the medium, this high temperature medium goes into a turban. In reality, this is high temperature of flu. Ghous I Centra pick Expansion takes place in the turban. The flue gas expands until it reaches the atmospheric pressure. The flue gas leaves the system at atmospheric pressure and gives its remaining energy to the surroundings. This step is a gamble that by heat exchanger in the heat exchanger the process is Isobe Eric So I Zubari Keat Rejection happens between state number four on volume. You can see that the compressor does work on the system on the turbine gains energy from the system by the medium that's working the turbine in the Rio Vert construction The turbine on the compressor have common shaft so the machin ery is drived by itself. The necessary heat is introduced to the cycle during combustion which is related to the heat exchanger between state number two country. The same idea of great on cycle can also be plotted In a ts diagram, the ice entropy, compression and expansion is represented by vertical lines. You can see that the isobars off the heat addition and heat rejection go under the ice, of course, which go 2.1 and two. If you recall the auto cycle, it uses the two dashed lines as it has answer Creek State changes in case of the disease. A cycle state number two entry is connected with an ice bar on state number one, and four is connected with an isil core, so the bottom dashed line would have been used off course. The temperature ranges at different, but it is good to realize how the cycles look like compared to each other. I summarized the basic relations for you in case off a berate on cycle. The easier solution is to model as an open system. Therefore, the change of an toppy ik first, the some of the heat on the shaft work. Be careful, and don't forget that shaft work is used in case of an open system. Now I need let the change off kinetic and potential energy. Usually this is a good assumption. The heat addition is done between state number two country as there is an ISA Barrick State change. The shaft work is zero, therefore the input heat equals to the change of inter happy. The heat rejection is isa Berrick to therefore it's shaft work is also zero. Be careful with signed as heat rejection has a negative meaning. Besides that everything is done, as in case off the heat. Addition, basically the absolute value of on top. It changes. They come between state number four and fun. The temperature ratio can be expressed by the half of pressure ratio for boost I central great compression on the expansion. The pressure ratio is an important perimeter. In case of the Brayton cycle, you must be family are with it. It is the ratio off the pressure maximum and minimum. The Tamerlan efficiency can be determined by the half of the pressure. Issue the terroristic a maximum off the efficiencies one, and you can see that the Tamela efficiency increases for increasing pressure ratio. Therefore, it is verse increasing the pressure ratio. According to this, however, in case of the Brayton cycles, we do not always want to increase efficiency. There is an alternative respect as the useful specific work has a maximum. Sometimes it is better to design the cycle to death maximum the useful specific work is the difference off the work gained from the turban and the work invested in the compressor or the specific work of the compressor equals to the change of anti P between state number funding to as the heat transfer zero in case of an ice entropy compression. Similarly, the specific work of the turban is the absolute value of the change of entropy between state number three and four. The two formulas are not the exact same as the sign of the work is different for a turban on the compressor. In case of a compressor, this work is given to the medium, So it is a positive burke in case of a turbine. This work is gained from the medium by decreasing its energy level. Basically, you can take the absolute value of these on top. It changes and you don't make any mistake with the signs the Maxima use with specific work is extracted from the system at a given pressure ratio value, it can be deducted. The maximum belongs to the pressure ratio that equal to t three over t one to the power of come over two times gamma minus, so either you can design a cycle to gain the maximum useful, specific work or to achieve the highest possible Tamela efficiency. Don't forget that I showed you the idea Cycle reality. The eye center pick. Efficiencies shall also be taken into account, as I have told you about it. In the lecture about efficiencies, losses occur both in the turban and the compressor. These decrease is the total efficiency on the useful work. 42. Brayton (Joule) cycle – Sample problem: let me show you a sample problem to practice calculations with the bright on cycle, an Idea Brayton cycle is investigated. The medium entering the compressor has Steven Temperature and P even pressure. The mass flow rate is am dot the medium interstate turbine a T. Three temperature. The pressure ratio off the compressor is R P. The medium is an idea gas. It's specific cast, constant is are, and it's a diabetic. Exponent is gum. We must determine the useful performance and the turmoil efficiency of the cycle. After that, the terminal efficiency must be determined in the known idea case when the compressors efficiency is given. In that case, every other data remains the same. The medium entering the compressor has a pressure off 100 killer Pasqua's on the temperature of 300 cabins. The must flow rate is five kilograms per second. The temperature off the medium entering the turbine is wonders and 500 gallons that is the third state if the first was the state before entering the compressor. The ratio of the pressures is down. The specific gas constant is 287 shoes per kilogram. Cabin. The Adia Batic expert. It's one point for the ice entropic efficiency off the compressor, or is 85%. In the second case, the idea cycle can be seen on the figure. You must use this in the lossless first case. The cycle starts with an ice entropy compression, for which the input, pressure and temperature is given done on ice. Abery heat addition comes, it's and temperature is known as it is the input temperature of the turban as the next day change is the eyes entropic expansion. The cycle is finally closed by an ISA Baraquio rejection. Let's calculate the missing temperature values first as we're going to need them if we want to calculate the changes of an toppy, which is needed for both for calculating heat on work, The and temperature of the compressor can be calculated based on the ice entropy compression. The temperature and pressure ratio have given connection during the ice entropic state change. The pressures are not known, but the pressure ratio is given so we can calculate the and temperature by the half of the initial temperature and the pressure ratio. The result is 579 cabins. The and temperature off turban can be determined in a similar manner, the same form lays used. But be careful with the pressure ratio, as it is Petri overpay for so the reciprocal is needed. For the present calculations, Petri equals two P two and P four equals two p. Von, according to the iceberg state changes. That is what I used to introduce the pressure issue to this formula. By rearranging the formula, the temperature off state number four becomes 777 cabins. Now we can calculate, or the heat on works appearing and the cycle Let's start with the specific eat addition. We need the eyes uber expensive ticket, which is an unknown perimeter. Yet we can calculate it with the usual formula based on the specific gas constant and the idea. Batic exponent the eyes upper expressively kid is 1005 shoes back kilogram cabin. The specific it addition equals to the change of entropy between state number two and three , as the heat addition is done in ice a Berrick manner. So the shaft work is zero. Input specific heat becomes the product off the iceberg, specific it and the change of temperature, which years 926 Kilo Chua sparking program Let's continue the calculations toward the useful performance. The specific eat rejection is again down in an Isa Berrick manner, so the first low off Dharma Dynamics reduces, and we get that the heat equals to the change of anti happy. As usual, the heat rejection has a negative sign. The result is 479 kilos. Julius Bar Kilogram. The use with specific work equals to the difference of the input and output heat or equals to the difference of the specific work of turbine on the compressor. Now we know the heat addition on rejection. That difference is 447 kilo Chua sparking program. The useful performance is the product off the mass flow rate and the use with specific work . It becomes too tells and 235 kilowatts. The terminal efficiency can be calculated right away as the ratio off the useful specific work on the specific E tradition. The result is 48.3 persons. Now we got all the answers for the first loss. Less case. Let's see the calculation with losses included, some quantities are modified. The ice entropic efficiency off the compressor shall be investigated first as that introduces the information about the losses. The compressor efficiency is the ratio off the idea. Andrea Change of entropy as the rial change of entropy is greater than in the one off the idea reversible case. In a compressor, we increase the energy of the medium. We put energy in the system. So in the rear case, we need to put more energy into the system to also cover losses. That is why the efficiency is calculated like this. You must take a look at the formula. With the temperatures, you can see that the rial and temperature is hired on the idea of fun. The and temperature off the idea case is already known as we calculated it previously. The rial and temperature of the compressor is the only unknown in the formula, so the formula can be rearranged and we can calculate the rial and temperature of the compress, or it becomes 600 funny. Eight cabins. Because of the loss is not only the input work, it's higher, but the heat addition becomes smaller. The specific eat addition can be calculated by the product of the as a correct specific eat and the temperature change just like before. However, the temperature change is smaller. S T two is greater. The specific either addition becomes 876 kilos US back kilogram. As the turban is still considered lossless, we can jump to answering the question. If you need to consider the ice entropic efficiency off the turbine to, you must calculate with it in a similar manner the use with specific work. It's still the difference off the input and output heat. The outward heat remains the same as before the input he'd changed. The useful specific work becomes 397 kilo Zhu, a spa kilogram. The turmoil efficiency of this case becomes 45.3% which is obviously the smaller than the efficiency of the previous lost last case. 43. Multiphase systems: in case of Multiphase systems, the system under investigation contents more than mom faces, which have different properties. Either they are states of matter differs, or even if the state of matter is the same, the properties of two phases can be significantly different. Give a materia can be in any off the faces. The change of properties off a giver material is through face transitions in case of first order face transitions. There is always latent heat, so either the medium transmits energy to the surroundings. Or it needs energy input from the surroundings to complete the face transition or so a sudden change of extensive state for I A bus occurs. For example, the volume off ice, water and steam are very different, even if the temperature and pressure is the same for the two phases, let me go to the first order of phase transitions there is mounting during with solid matter becomes liquid. During operation, the liquid becomes guests during sublimation so it becomes guests without being in liquid state. These three face transitions need external heat input from the surroundings that additional heat covers the energy need off the particles with which they can go to a higher energy level. During freezing, the liquid becomes solid During condensation, the gas becomes liquid, enduring the position the gas becomes so did without being in liquid face. These three face transitions release he to the environment mean by the particles, go to a lower and an angel ever record Civilization is also first order face transition. It is the transformation from once lit face to another. The properties of these two states are very different from each other. Besides the first orders face transitions. There are second order phase transitions to there is no latent heat and the excessive state for IAB hours do not change suddenly during the face transition, however, the properties off phases are different. Such second order phase transition happens in the Curie Point off the federal mine attic Matt Areas In the Curie Point they become para magnetic, which is a change of the magnetic properties. So there is really a face transition. Also, superconductivity is reached during a second order phase transition below a critical temperature, the material via conduct electricity without losses. These are just examples I could save anymore. But now I concentrate on the first order of phase transitions as they are more significant in terms of dynamics so far. I always talked about actual Librium and quasi static state changes, so we do the same in case off motivates systems. The actually room is investigated between faces. For simplicity, let me talk about a two faced system with one component. The actuality off intensive state for I A bus is needed for the actual Librium between faces. Therefore, the temperature. The pressure on the chemical potential is the same in both faces, and also they have homogeneous distribution within each face for inner. Actually, Librium, the line of factory Librium, or so called face boundary, describes the actually broom off two phases. We can use the line as there is only one degree of freedom on the face boundary, according to gives his face through. Therefore, either the pressure is a function of the temperature or the temperature is a function off the pressure. Either way, one intensive state, meribel, is enough to describe the state. The pressure of the points on the face Bonder s called saturation pressure and the temperature is the saturation temperature by putting the lines of actually broom or so called face boundaries, we get the face diagram. There are three phase boundaries on the face diagram. The sublimation line separates the solid and vapor face. The matting land separates the solid and liquid face. The evaporation line separates the liquid and vapour phase. The three lines have a common point. It is called the Tripper Point In the Tripper point. All of the faces are present, so there is solid liquid and vapour at the same time. It is a valley find point with constant physical properties. Therefore, even temperature scarce can be attached to a trooper Point exactly that is down with a three per point off the voter. The other very important point is the critical point. That is the end point off the evaporation line above that point. There is no point talking about evaporation line as the liquid and vapour face have the same physical properties. Therefore, you can make a process which goes from vapor face to liquid face or with Savar PSA. Without face transition, you just have to design the process in a manner to go around the critical point above the critical point. Also record the medium gas instead off raper, there is only terminal logical difference between them. You cannot notice any sudden change of properties between paper. On gas, there are basically two different shapes off the face diagram on the one on the right hand side. It is true for every phase boundary that the temperature increases with increasing pressure . This is always true for the sublimation on evaporation lines. However, in case of the matting line, the opposite can also happen. The temperature can both increase and decrease for increasing pressure. For example, the voter behaves according to the diagram on the left hand side. If the pressure is increased on the eyes, it mats at a smaller temperature. This haps you. If you go skating, you concentrate your weight on a small area. The I smart and you can basically slide on a tin voter for him. The face diagram can also be plotted in PV coordinate system. In this case, the face Bonder has become areas instead, off lines or so the three per point becomes a line. However, everything is the same. The same face transitions happens. There is a transition between solid and liquid, so that vapor and also between liquid and vapour, faces above the critical temperature gas face exists on the liquid vapour transition can be avoided by going around the critical point from above. There is a need to define a new quantity in the mixture zone to have unique description off the state. The ratio of the states shall be defined. It can be calculated as the massive one face divided by the total Thomas, which is actually the some off the mask off the two phases in a give a mixture zone. This ratio is mostly used in the liquid vapour mixed zone, and it is called vapor quality. The vapor quality is the mosque off the vapor, divided by the sum off the mass of the paper and the liquid in the liquid vapour mixture zone. You can only calculate with wet raper for the calculations. The vapor qualities used the excessive quantities can be expressed by its harp on L index marks the quantities valid for the saturated liquid state. The saturated liquid state is the state on the side of the liquid where the vapour content is zero G index marks. The quantity is valid for the saturated vapour state. This means the state on the other side of the picture zone, but the liquid content is zero and only vapor is present. G is used as an index to mark the gas constant, but it is not a correct terminology. Please rather use vapor when you refer to this face. In case of a wet paper, you can use the following formulas to calculate the excessive quantities with a golf notations. The formula is basically the same. Let me tell you it through the example of a specific volume, you take the specific volume off the saturated vapour and you multiply it with the raper quality. Don't you add one minus the raper quality touch the specific volume off the saturated liquid. One man is the vapour quality. Is the ratio off the liquid content? Actually, so the vapour content has a property and the liquid content has another property. They can be added by multiplying down with relative content off each face. The anti P and entre pre can be calculated in the same manner 44. Two phase medium – Sample problem: let me show you how to calculate in case of a to face medium a to face medium having a mass and he even pressure is in a container off the volume. Que heat is rejected from the medium after the heat rejection. The pressure of the two first medium is P two. It's an Tapie's age, too at p even pressure the specific and up if the saturated liquid is age l and the saturated vapors specific and happy is age G. We must determine the mass off each face at the initial state. The volume of the container is one cubic meter. The mass of the medium is dang kilograms. The initial pressure is 500. Killer past cast on pressure is 150 kill of Pascal's between them. Want house and kill a juice off heat is rejected from the medium. The anti P of the medium at the end state is 5000 kilos. Users at the vampire assured the specific and top of the saturated liquid is 200 collage US back kilogram and the specifications top of the saturated vapour is 2000 kilos US. Back kilogram. In the first step, the initial anti p shabby, calculated as the ratio of the faces can be expressed from that quite easily by using the formula off the vapor quality, let's think about what kind of process happens. There is a closed system as the whole process takes place in a container. As the volume of the container is fixed, the volume off the mixture also remains constant, so there is an ISA correct state change. We can take the heat rejection into account by the half off the first law of thermodynamics . According to the first law of thermodynamics, the change of internal energy equals two minus one times the rejected heat. Internal energy appears as there is a closed system. The external work is zero as as a correct state change happens and the heat is negative as it is rejected from the medium, the anti P can be written according to its definition. The formula can be riff return for the change of anti happy. It equals to the change of interna energy, plus the product off the change of pressure and the constant volume In the second term. Only the change of pressure appears as the volume miss constant in general case, the change of the product of the pressure and the volume must have made they come. The formula can be rearranged to calculate the initial and happy the initial and therapy equals to the anti P of on ST minus The change of internal energy Man is the product of the change of pressure and the constant for you. The New America. A result, it's 6350 kilos shoes. Now we are close to obtain the vapor quality. The initial specific ANTAR P is the ratio off the initial and toppy and the totem us. So it is 635 Collage Lewis backing program. As both the entropy of the saturated liquid and vapour is known, the paper quality can be expressed by the anti appease. The paper quality equals to the difference off the actual specific anti puppy and the specific anti P of saturated liquid over the difference off the specific and UPI of the saturated vapor and liquid. This formula can be written similarly with specific on trapeze or specific volumes. The paper quality is 0.242. The mass off each face can be expressed now, the mass off raper is the product off the paper quality and the tow Thomas. It becomes 2.42 kilograms. The mass off liquid is the remaining part, the difference off the total mass and the mass off paper it becomes 7.58 kilograms. 45. Phase diagrams of water: water is the most commonly used medium in case of multi face processes. It is useful to be family here with the face diagrams off water. Let's start with the TS diagram as that is used. Most often, the saturation don't means the face boundary off liquid and vapour to the left of the dome . Liquid phase exists on the right side, vapors percent in between. Under the dome, there's liquid vapour mixture. The critical point is the highest point off the dome, as the highest temperature belongs to the critical point above that record the medium gas Instead. Off paper, it is useful to know how the important special processes look like in the diagram. Obviously, the horizontal lines are isa terms. On the vertical lines are eyes and throats, as it is a ts diagram. I marked the isobars re trad above the critical pressure. The isobars do not go under the dome, but below the critical pressure. They entered the dorm in case of the two face medium. The constant temperature also means constant pressure, and the constant pressure also means constant temperature, so the eyes of bars are also horizontal. Under the dome before and after the dome. The isobars are hyperbolic the eyes, of course. The constant volume lines are marked with blue color under the dome, The steepness off the ice, of course, the crease above the dome. The steepness increases. The eyes, of course, are always steeper than isobars. If they go through the same saturated raper point the ice Zantops the lines with constant and happy unmarked with clean. These shall be used in case off throttling they are or he parabolic. I need to show you one more thing. I might the constant raper quality lines with blue. If you take 0.1, you can calculate its extensive state where I of us by the help of the vapor quality on the state where I a bus at point from l and 0.0.1 g. The paper quality can be expressed by the half of the specific Williams, the answer peas and the an trapeze. The distance between 0.1 l on bomb, divided by the total distance between point fungi on van L equals to the vapor quality, which is actually the ratio off the mass of the raper and the Thomas of the two faces. Let me show you another important diagram. It shows the logarithms off the pressure as a function of the anti poppy. A dome appears here, too. It is a slightly different shape, but the critical point is the highest point here. The horizontal lines are isobars and the Vatican lines are ice on tops. I marked the ISA terms with red color. They are very steep in the liquid face. Done. They are horizontal in the wet paper face as the temperature and pressure is constant at the same time. In the vapor domain, the pressure decreases with increasing anti happy. Along the ISA terms, the higher the temperature is the hired Isa Tam Ran's. It is important to note, as in case of the specific volumes, the opposite is true. The higher the specific volume is the lower dicer Koran's. You can see it on the blue lines. The ice on troops are marked with green lines. They are very steep, almost vertical lines. If you go to the right, the entropy is greater. There are several more diagrams which are used in practice. Most come only you can see two Yes, and look be age diagrams. But there are further diagrams like the PV and the age s on the T Age diagrams. All of them are empirical diagrams based on measurement, so you can find such diagrams in the late nature for basically any material, the constant lines are usually marked, so you can easy and navigate on them. 46. State changes of water - Sample problem: let me show you how to handle problems related to the state or face changes off water saturated water with, um, that mass flow rate and even pressure is throttled two p to pressure. This means that on ice and topic process takes place. Then the phases are separated so the water content is carried away and only the vapour content is used further. The acquired vapor is expanded in a turban to Petri pressure. The inner efficiency of the turban is dirty. We should calculate the paper quality after the throttling, and then we should determine the performance off the steam turbine. The mass flow rate of the saturated water is one kilogram over. Second. The initial pressure is 160 bars. The pressure after throttling is 80 bars. Finally, the pressure after the expansion off the steam is seven kilo Pasqua's the efficiency of the turbine is 93%. There are three important pressure lovers for which the voter properties unknown. As we are working in the mixed voter vapor zone, there is von temperature value for one, given pressure value a side of that, the specific and be the specific an therapy and the specific William off the saturated water and the saturated vapour are known. The one common marking refers to saturated voter on the two comma marking refers to saturated vapour. These data could always be found in voter data tables, so you can always use them if you need to calculate in practical problems to get an overall picture, I have thrown the TS diagram off the whole process. This step always have to summarize the task we need to go through. The marked process is the starting point is at the saturated voter side of the mixed zone. The saturated voter is on the left side of the curve on the saturated vapour is on the right side of the curve. We know the exact temperature value, but now it is enough to get the trends. We start from higher temperature and then the temperature decreases. The first process is struggling in case of trickling the anti RB or specific anti peas constant. It is an ice and topic process. So when I sent up, connects state want to stay two as it can be seen on the diagram. After throttling, the faces are separated. There is saturated voter and saturated vapour at ST to the raper quality specifies the ratio off the mass of the raper to the total mass. But we separate the phases. We get saturated water and state do come up and we get saturated vapour at ST to do comma. The next process only uses the saturated vapour. The expansion can certainly be considered at the aerobatic. As the process is quite fast. There is no time for heat exchange if there would be heat exchange. The test description would have to specify that there is actually a heat transfer to or from the system, so there's an idiomatic process with which we cannot calculate directly. We can only connect the rial process to the idea by the help of the turbine efficiency. That's why I drew the idea line. There is a reversible at the robotic process in the idea case, so an ice and troop connects to two comma 23 idea. The entropy changes zeroed this Linus vertical. In reality, there is some entropy increment. Therefore, the other robotic process ends in three, which is located at the same pressure as three ideal. But the entropy off three is greater. Now. We haven't overall picture we can calculate with startling to get the state number two. Then we calculate the paper quality, which defines the raper mass at 22 comma. That amount off raper is expanded and we can calculate the performance of the turbine. So let's start with throttling. The pressure of the initial state is 160 box. We know that initially the whole medium is saturated water. We can use the data table to get the specific an therapy or any other property off the first state. Now the specific and therapy is the most important. One is the centerpiece stays constant during throttling. Based on this information, we know the specific and happy. In the second state, this haps asked to place state number two on the horizontal line belonging Topi to pressure . We know the specifications. Happy off saturated voter and saturated vapour at Peter Pressure based on the data table and we know the specific and therapy at ST Number two. The paper quality can be expressed based on the specific and up is that we know we can substitute into the formula for the vapor quality. The difference off the specific anti p of the given point and saturated water is in the nominator. This is divided by the whole length of the horizontal line that land equals the difference off the specific. An therapies off saturated water and saturated vapour, 23.1% off the mass Off the medium is saturated vapour in state two. This is an answer for the first question on also we need the mass of the vapor that goes into the steam turbine. Now we can investigate the expansion. There is saturated vapour at ST to two comma. This goes into the turban. We know all of the important properties at this state. It is included in the data table. We should calculate the performance of the turbine. The performance equals to the product of the mass flow rate of the medium and the specific anti change. The absolute value shall be taken if the performance off the turban is the amount that we want to calculate. The interpret change of the medium is negative, so the medium lose those work to the surroundings. The shaft word is negative. If we look from the perspective of the medium, this is the performance that the turban gives to the medium. However, the turbine purse four months is what we can use later as mechanical performance. Therefore, it is a positive quantity that the medium gives to the turbine. The mass flow rate off the paper is needed as only that amount of material goes into the turban. The mass flow rate of the way Paree first the product of the paper quality on the total mass flow rate as the raper quality equals the ratio off the vapor mass on the total mass off the media. So only 0.231 kilograms of raper goes into the turbine in one second. The rest of the mass flow rate is saturated water that's carried away. Now we need one more data, the really specific and of change the rial specifications. Rapid change appears in the turbine efficiency formula. The ideal specific and a bit change could be determined first, and then we can calculate the rial change based on the efficiency. What do we know about the idea process? It is ice entropic. The entropy doesn't change between 22 comma and idea third state. Therefore, the specific answer pee off the idea. Third state is known as the special began to be of 22 Comma is in the data table. We can calculate the vapor quality at the third state and we can express the specific Antebi from the paper quality as we used it Previously. The vapor quantity can be calculated business specific anti copies the specific and up with the idea towards status unknown, such as the vapor qualities unknown but the raper critic and be ex presidents of RAV A's we can just calculated based on the specific an trapeze we know the specific and European the idea. Third state on, We have the specific kantra p of the saturated water and saturated vapour at Petri pressure from the data table. Formally, the formula is the same with an therapies and an trapeze. We can substitute on find that the paper quality eat 1st 0.6 and it's 72. In this case, as we know this, we can express the specific and happy off the idea. Third State 1780. To kill a Jewess over kilogram is the specific Antebi after the ice and traffic process. Based on this, we have the ideal under be changed during the process, we can substitute into the turbine efficiency formula. In the Rio case, the specific and up it change equals to the difference off the specific antibodies in state three and two comma. In the ideal case, the idea Dirt State under do do Coma state is used. The specific Antebi off the rial third state can be calculated as we know the turbine officials. The result is wanders and 100 50 kilos Jewess over kilogram. This can be substituted into the turbine performance. Former or we could have just expressed age two to command minus age. Tree difference. Most importantly, we can calculated performance as we need an absolute value. Actually aged three sub started from age two to command to get a positive result. The performance off the steam turban is 210 kilowatts. The chef performance that act on the steam would be miners 200 kilowatts. Be aware off the signs 47. Rankine (Clausius) steam cycle: in practice, One of the most important cycles is the ranking steam cycle. Sometimes it's called ranking closed cycle, but you can use Rankine cycle to refer. Just don't be surprised to hear it in another way. The cycle is used in power plants, so lots of the energy that you use comes from a Rankine cycle. First, let me show you the physical layout off a basic Rankine cycle. Let's start from Point Number two from their liquid is going into a boiler where heated Isha happens. The liquid ever parades, and it is also superheated. The output of the boiler is vapor, with high pressure and temperature. It is going into a turbine where it is expanded and its energies extracted. At this point, the output is still waver or bad paper. It can be released to the environment. A new liquid can be pumped into the boiler. The efficiency is increased. By closing this cycle, the vapor coming out from the turbine is condoms. On this condoms voter is pound into the boiler during the cycle. The heat addition happens in the border. The work extraction is done in the turbine and the heat rejection in the condenser to operate the pump. Some work must be used, but it is negligible. Competitive work extracted at the turbine On the figure I might the vapor with a ticker lined and liquid. But I also wrote face state everywhere. The cycle can be plotted in any of the diagrams, but first, let's summarize what happens. The heat transfer is Isa Barrick, both in the boiler on the condenser. The expansion in the turbine and the pressure growth in the pump are both eyes and tropic. In the idea case, you can see the idea cycle on the diagram. It starts from the saturated liquid state at 0.1 between states. One into the pressure is increased in an ice entropic manner by the pump. Then the liquid enters the boiler, where Isa Baraquio tradition happens. The fluid goes 2.3 on the ISA Barak line, according to this heat addition. First, the saturated liquid status reached than the whole a medium have operates. At that point, we arrived to the dry saturated vapour state. The actual Rankine cycle operates. Until that point, the dry saturated vapour would go into the turban for expansion. The Rankin close your cycle use super heating, and it goes on t appoint tree. At that point, the superheated vapor enters the turbine and expands in an ice entropic manner. State number four can be at a vapor or vet vapor state. The more droplets appeared, the more erosion is done on the turban, so you should avoid droplets as much as you can. Therefore, high paper quality off point for is advised. Finally, the raper, or wet paper enters the condenser in which condensation happens in an Isa Berrick manner. This takes the vapor back to the saturated liquid state. Then the cycle starts over. Let me summarize the formulas for calculations. You can consider an open system for which the first law of thermodynamics Camry of written with the change of an toppy and with shaft work. This is advantages, as the shaft work is zero in case off isil bark state changes. The heat addition is the change of anti P between state number tree to as the shaft working zero at that ISA Barrick State change. Similarly, the heat rejection is the change of anti P between state number four and fund. The entire P cannot be calculated as simply as it was for gases. If every point is given the answer, peace can be found on the diagram. In practice, you must measure or find my German data for your problem. The useful specific work is the difference off the work extracted in the turban and invested in the pomp. The specific work off the turbine is the change of an toppy between state number, tree and for is there is no heat transfer during the ice entropy expansion. Similarly, the specific work of the pump is the change of entropy between state number fun and to finally, the thermal efficiency is the ratio off the useful specific work on the specific heat addition. The useful specific work is either the difference of the input and output heat or the difference off the work of the turban and the bomb. I quickly summarized the rial cycle for you in the rear cycle, you must consider closest to the cycle starts from 0.12 point two as the pump takes the liquid to the boiler. In reality, the pumping is irreversible, so you cannot reach point number two. But you can only reach to coma, which has a slightly greater an therapy in temperature at the same pressure. From this, the medium shop heated until a given temperature. I mean, why flow losses occur in the boiler, which decreases the pressure so the process does not follow the ice a bar instead of that, the desired temperature. It's reached at three comma, where the pressure is smaller and the entropy is greater. Also, more heat input is needed to get to three comma than to get 2.3. Then comes an irreversible expansion 2.4 comma. There is also pressure drop in the condenser. So the state change is not Isa Barrick either you can find four comma by considering that 40.1 shall be reached after the pressure drop. In reality, it is important to minimalize thes losses. It is especially important considering that a small increase in efficiency means a lot of money in case off power plants 48. Rankine (Clausius) steam cycle – Sample problem: calculations with steam cycles are even more complex than the vans with guest cycles. Let me show you a sample problem with an idea steam cycle. In case of the known idea case, you can take losses in account by the half of the ice. Entropic efficiencies off turbines and compressors. Now on idea. Rankine cycle is investigated. The pump increases the pressure off the income. Possible water from P one to P to the vapor exiting the boiler has teeth three temperature H tree specifications happy and asked three specific entropy. The expansion in the turban is ice and tropic. We must determine the useful specific work, the terminal efficiency off cycle on the mean temperature of the heat. Addition. Basically, we are going to have to calculate everything in the cycle. Step by step. The initial pressure is tanking Pasqua's. It is increased to 150 bars by the bomb. Then the temperature off the medium increases to 700 degrees. SAS is in the boiler. The super heated steam has a specific and UPI off 3700 kilos. Julius Bar Kilogram andan entropy off seven kilo Jewess back kilogram cabin. An additional table is given, which contains all the necessary data to calculate with the face trans issues. The smaller pressure belongs to the condensation. The higher bomb belongs to the operation for boost pressures, the temperature off the voter steam mixture of faces given, or so the main properties off the saturated liquid and saturated vapour are given. These are the entropy, entropy and specific William Values on l Index marks the properties off the saturated liquid. G index marks the properties off the saturated vapour before serving the problem. Let's take a look at the idea cycle between state number one and two. The pressure is increased. I sent, typically by a bomb. According to the problem description, the water is considered to be income possible. So the volume Miss Constant during this part of the cycle between states number two entry on isometric heat addition is done in the border. Date are given in ST Number Tree between state number three and four, and I sent a big expansion is done in the turbine state number four. Is that the same pressure of state number one as there is a nice Bereket rejection, a condensation between them. Let's exa mined the cycle. The first step is to pumping. The work of this step is needed to calculate the useful work we can only calculate with specific quantities as no external state reliable is given. So we calculate the specifics. Shaft work of the bomb. The shaft work is calculated as it is easier to use an open system for calculations. The integral is easy to serve as the specific will you miss constant Due to the income possibility off water, The specific volume off state number of on is known as it is exactly the specific volume off the saturated liquid at the lower pressure level from the table, the pressure of the starting on states are known, so the shaft work becomes 15 kilos US back kilogram. The change of an toppy equals to the shaft. Work off the pump. According to the first law of thermodynamics, there is no heat transfer as the pumping is a diabetic on. The work is considered to be positive, as this work is done on the system to increase its energy mean by the pump increases. The pressure, the specific an toppy off state number two can be expressed. The specifics shaft work off pumping is known on the specific and toppy off. State number one is also given in the data table. In the next step, the medium goes into the boiler boots and points of the state are known, but we still need to calculate the specific eat addition as it will be useful when we want to calculate the thermal. Official C. The specific heat addition equals to the difference off the anti p of two and points off the ice Abric state change this camps from the first law of thermodynamics as the shaft workings Euroforum isa barrack process. The result is 3505 kilos US back your program. The next day change happens in the turban and it is a nice entropy expansion. The starting state of the expansion is known, but the entropy of the in state shall be determined to open the work of the turbine. We know that the state changes I Centra pick, so there is no heat transfer and the entropy does not change. Now we can use the second fact the entropy of the in state equals to the entropy of the starting state. Therefore, the entropy of the and state is smaller than the entropy off the saturated vapour at the given pressure level. This means that the and state of the ice entropy expansion is somewhere in the voter steam mixture zone. Therefore, the vapor quality shall be calculated. It can be expressed by the half off on trapeze. It is a van on the creation which uses proportionality. The paper quality becomes zero point 803rd Yvonne. The vapor quality can also be expressed by the hap off anti appease. Basically, the same formula is valid, so data are known at the pressure level off state number for the specific and copy can be expressed. It becomes 2190 van killers. Us back your program. With this, the specifics sharp work off the turban can be calculated. It is the difference of the UN therapies off state number four country. According to the first law of thermodynamics, the result is miners wanders on 509 kilos US back ilo Graham. The result is negative as this amount of specific work is extracted from the medium. So actually, the work off the turban is the absolute value off this result. Finally we arrived to the condoms are the heat Rejection can be calculated here. It equals to the change of an therapy. We can use the absolute value as the result would become negative. But the negative sign is included in the terminology. The result is tutors and 11 kilos US back kilogram. After we investigated every step in the cycle, the questions can be answered quite easily. The useful specific work can be calculated in two ways, so we can even check or result. Either you can take the difference off their input and output heat or you can take the difference off the shaft works off the turban and the bomb. The result is 1494 kilo joules per kilogram. The terminal efficiency is the ratio off the useful specific work on the input heat, it becomes 42.6%. The mean temperature off the heat addition is the ratio off the specific thick heat addition on the change of entropy during the heat Addition, this formula already appeared in the lecture about the active on camera cycle. The entropy off state number two equals to the entropy off state number from as there is an ice entropic state change between them in ST number from there is saturated liquid at a given pressure for which the entropy can be found in the table. The mean temperature off the heat addition is 275 degrees SAS is. 49. Improvement of efficiency: let me briefly introduce you to the efficiency optimization off the steam cycle as it has a great significance in practice. As the analyzes can be done by soft words, it is easy to try out any combination of the methods, so there's always a chance of finding uneven, better solution. If you can't find him, you can be a millionaire. So good luck. Let's recall the equivalent Carnot cycle. There are two possibilities for increasing the efficiency. Either by increasing the temperature of heat addition or by decreasing the temperature off heat rejection. The 2nd 1 can recovered more easily. In the present case for the Rankine cycle, the heat rejection was firstly done in the environment as an open system was operated in the earliest steam engines. The application off a condenser was the first step off improvement in a condenser. The heat rejection is totally under control. The heat dejection is ice a brick, and it is also ISAT Irma as there is a face transition. Therefore, the mean temperature on the minimum temperature are the same. To increase the mean temperature, there is only one solution. It is done by decreasing the pressure off the condenser If you decrease the pressure, the temperature also decreases as we can go far below atmospheric pressure. The efficiency can be increased greatly. However, there is not much room for further improvement. The temperature of heat rejection is already optimized in modern devices. However, there is still some room for improvement if you want to increase the temperature of heat addition, there are several solution methods that you can perfect and apply the timer dynamical possible. Maximum efficiency is close, but the slight improvement can also save billions of dollars and also a lot of energy. Super heating is the first natural matter of increasing the mean temperature of heat. Addition, the higher temperature is reached the higher deficiencies, but there are limits due to the applicable materials. Even the best materials cannot withstand any temperature. So until the material science does not provide better materials to apply in boilers and turbines, the maximum temperature is basically given. However, the mean temperature steer has to be improved as it does not equal to the maximum temperature. The mean temperature of heat addition can be increased by pre heating the feed voter by tapped hot steam from the turbine in this matter. The hot steam enters the turbine. Does some work on Done apart off It is stopped and used for pre heating. While it is still at a high temperature off course, the rest of the steam goes through the turban and the rest of the cycle. The main point is to achieve that the feet voter enters the boiler at a higher temperature , so the heat addition start at a higher temperature. In this way, the mean temperature off heat addition increases the cycle. Applying this mattered ISS good regular relative ranking cycle. The other main mattered is the reheating. The medium is expanded in the turban until a certain point, then the whole medium is reheated on the expansion continues in an other turbine. By applying several stages, the medium can be reheated a couple of times. The other practical advantage of this mattered is that it ever. It's working in the voter steam mixture zone, which is good for the durability off the turbines in engineering practice. Already, almost the best possible efficiencies reached. But go out there and do it even better. 50. Refrigerator, heat pump: the refrigerator and the heat pump are basically the same. The only difference is that they are used for different applications. Most of them absorbs heat from quarter space and release it to a former space. In case of a refrigerator, the temperature off the colder place shall be decreased. In case of a heat pump, the former place shall be heated. The terminal efficiency is not suitable for characterizing the refrigerators and heat pumps . The temporal efficiency would be greater than one based on the usual definition, as the useful quantity can be greater than the external input quantity. To see this, take a look at the energy balance. In case of the cycle, it is observed from one side, which means the heat input or so some extra never kiss nated. The some of these means the heat output, which is released to the former space. The coefficient of performance characterizes the refrigerators well. In case of cooling, the definition is different than in case of heating. The coefficient off performance for cooling is the ratio off the absolute heat input and the accent of work. As in case of cooling, the useful quantity is the observed heat on. We need to invest a given amount off work to achieve the goal off Observing the heat. The coefficient off performance is usually greater damn fun. The usual notion is C O P. But you can also see absolute at some countries in case of heating, the coefficient off performance is different. It is the ratio off the output heat on the accent of work. In this case, the useful quantity equals to the heat released to the space, which needs to be heated as the heat output equals to the work, plus the heat input. This measure is always greater damn fun. The simplest heat pump works according to the reverse Carnot cycle. In reality, you can achieve a perfect reversed Gunnell cycle, but it it's the understanding the process starts from the mixture zone on as a term. A heat addition happens in the heat exchanger between state number one and two. This means evaporation off the medium, so it is not only Eissa Thoma but as a barrack to the heat is observed from the quarter space. In this stuff done, a nice entropy compression comes. The extent of work is introduced to the system in this stuff. The temperature is increased by the half off. This external work at the higher temperature, another ISA term. A heat transfer happens in the heat exchanger. Now the medium releases its heat to the environment. This basically means Condon ization, and ideally, it is done between the saturated vapour and saturated liquid states. Finally, on eyes entropic expansion completes the cycle. During the cycle, the heat is successfully transferred from 1/4 space to hotter one. Actually, you get the same result. By reversing any off the cycles that you have learned about, let me show you the reversed date on cycle. As it is important in practice, the cycle is almost the same as the reversed carnal cycle. Let's start from ST Number Fund, which is in the mixture, So an answer. Baraquio Tradition and evaporation takes the medium to the saturated vapour state. The state number two. In this step, heat is absorbed in a heat exchanger from the surroundings, which will be cooled in the next step on ice entropy. Compaction is done in a compressor for six off simplicity. A reciprocating compressor is more than enough for this process. In this step, external work is introduced to the system, which enables the next heat transfer between state number three on for the medium is condoms, during which answer Barrick he'd rejection takes place. He is released to divorce her space. Finally, the cycle must be closed. It can be done by an eye. Central big expansion in a turbine this matter has a great practical drove back. The high water droplet content erodes the turbine. Therefore, a turban could not withstand this operation for long. In practice, troubling is used instead off a nice entropic expansion. By trickling, we go from state number for two state number van coma in an ice and topic manner. This solution decreases the amount of possible heat absorption, but the lifetime off the heat pump or cooling device is greatly increased. Therefore, in practice, there is an ice abric heat that the sham by heat exchanger. In the first, it is absorbed from the space which are be cooled in the second step. Reciprocating compressor does work on the medium to increase the temperature at the higher temperature. Heat is really raised to a space which has a higher temperature than the one which rebounding to cool down Finally, the cycle is goes closed by troubling, which decreases the pressure while we cannot gain any work from the process. If you want to calculate, you can do the following. You can calculate the heat input as the difference off the answer. Be off state number two and BankAm. You can calculate the external work as the change of anti LP between state number three. To finally, the heat output is the difference of the anti P off state number T and for this can also be written as the sum off the heat input and extra network. This results in the difference of the enterprise of state number three and vocal as the answer. P of state number four and Val Coma are the same. The two formulas are active element. After he obtained the heat's on the work, you can calculate the coefficient of part four months. Be careful and use the formula for cooling. If you want to operate a refrigerator and use the formula for heating, if you want to operate the heat power 51. Coefficient of performance – Sample problem: let me show you a sample problem to practice the application of coefficient off performance , most in case of cooling and heating. The coefficient off performance off a heat pump is given. The working medium is condensed a T out temperature. I used this index as the heat outward belongs to the condensation. We must determine the mean temperature off of operation, which actually means the mean temperature off the heat Input as the heat is absorbed from the environment during the evaporation off the medium or so, we must determine the coefficient off for four months. If the device is operated as a refugee writer, please remember that the coefficient of performance is different. In case off refrigerators and heat pumps, there are not much data. The coefficient of performance for heating is for the temperature of condensation is 70 dig recesses. This is worse converting to cabins, the definition off the coefficient off performances needed for calculations. It can be returned based on the energy balance. A heat input and the extent of work goes into the system, and then output heat comes out in case of cooling. The coefficient of performance is the ratio of the heat input and the external network as the aim of cooling is the heat absorption from the space which needs to be cooled. The afford. The useful quantity is the observed heat and the input quantity is the external work. The work can be expressed based on the energy balance as the difference off the heat, output and input. We can define a mean temperature for boost the heat input and output. So basically we can think off ice a term A processes according to that the heat transfer can we've returned by the half off temperatures as we can simplify by the change of entropy . The coefficient off performance of cooling is the mean temperature off the heat. Input over the difference off the mean temperature off the heat, output and input. In case of heating, a similar formula can be found. The useful quantity is the heat released to the former space, so that is divided by the work. The work can again be expressed by the heat transfers and the temperatures can be substituted. The coefficient of performance off heating is the mean temperature off the heat output over the difference off the mean temperature off the heat output and input from the formula that we obtained. The mean temperature off of operation can easily be calculated as it is the only unknown after rearranging the formula. We get 257 cabins or minor 16 degrees off. SAS is as a result, so the medium is evaporated at that temperature. The coefficient off performance is already known for cooling. We only need to substitute the temperatures. The result is tree. If you remember, the C. O. P was four for heating. You can write the formula generally, and you can prove pretty quickly that the difference off the two formulas is always one. In case off heating, the heat out with appears in case of cooling. The heat input appears. If you take the difference, the heat's dope out off the creation and only the ratio off the work by itself remains. It is off course bomb. If you know this result, you can use it for making the calculations faster 52. Refrigerator - Sample problem: that's see a sample problem with the refrigerator. The coefficient off there for months off the investigated refrigerator is given. The refrigerator takes school in specific it from the cooled space at the in temperature. Taking the heat from the good space means the heat addition that happens from the perspective off the refrigerator. That is why we should write Coup in entity in coup. Out and t out would relate to the heat rejection of the refrigerator, where the refrigerator is schooled and the surroundings are warmed. The mass flow rate of the cooling medium is, um, that the cooling cycle is closed so this mass flow rate occurs at every operation stage. We must determine the mean temperature off the heat rejection, the specifications rejected from the refrigerator and the mechanical performance that is needed to operate the refrigerator. The coefficient of performance requested. Three. The temperature of heat addition is 200 63 cabins. The specific input heat, which is taken from the court medium, is 120 kilo Chua sparking program. The mass flow rate is 0.1 kilograms over second, let's start a solution by calculating the mean temperature of the heat rejection in the topic off refrigerators and heat pumps. We should always use the formula for the coefficient of performance. Let's use that the confession of performance requested the ratio off their input hit on the work in case off cooling. The useful amount off this process is the heat that is taken away from the court space, and the input amount is the mechanical work that is used for operating the refrigerator. In case of cooling both the input heat and the heat coming from the mechanical Burke should be the least towards the surroundings. Therefore, coup out equals the coop in Plus W rearranged this creation and substitute w by coup out minus school. In you can write mean temperatures instead of specific heat as they only differ by constant multiplier. Now you can see all of the creations that were snowing. To get the mean temperature of the heat rejection, we must use the term situation. After rearranging the recreation, we can calculate the mean temperature related to heat rejection or, he doubt put. The result is 350 won cabins. The specific rejected heat can also be calculated from the basically creations. This heat appears in the second equation that should be rearranged. The equation is very similar to the situation off the temperatures. The only difference is that specific. It's appear instead of temperatures. The specific rejected heat is 160 Qinzhou US over kilogram. The mechanical power for months is the last unknown that we need. The mechanical performance is the product off the mass flow rate and the specific work. So we have to express the specific work. We could use either the energy balance or the formula of the coefficient of performance based on the coefficient of performance. The mechanical work equals the ratio of the input eight on the coefficient of performance of cooling based on the energy balance, the mechanical work is the difference off the output and input hate. Either way, the result is 40 kilo joules over kilogram. This camp, um, were deployed by the mass flow rate to get the mechanical performance. The performance is four kilowatts