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Thermodynamics - The science of energy transfer

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Lessons in This Class

37 Lessons (3h 51m)
    • 1. 01.Thermodynamic System

    • 2. 02.Thermodynamic Processes

    • 3. 03.The laws of Thermodynamics

    • 4. 04.Work transfer

    • 5. 05.Sign convention of work

    • 6. 06.Work as a path function

    • 7. 07.PdV work for various reversible processes

    • 8. 08.Polytropic index n

    • 9. 09.Heat transfer

    • 10. 10.Work apart from PdV

    • 11. 11.I Law of Thermodynamics

    • 12. 12.Energy as system property

    • 13. 13.Energy as a system property

    • 14. 14.Enthalpy

    • 15. 15.Heat transfer in isobaric and isothermal process

    • 16. 16.Heat transfer in adiabatic and polytropic process

    • 17. 17.Numerical I law

    • 18. 18.What is a open system

    • 19. 19.Mass flow rate

    • 20. 20.Energy flow rate

    • 21. 21.SFEE derivation

    • 22. 22.Nozzle and diffusers

    • 23. 23.Turbine & compressor

    • 24. 24.Throttling Process

    • 25. 25.Heat Exchanger

    • 26. 26.NUMERICAL on SFEE

    • 27. 27.Heat and work transfer in open system

    • 28. 28.Work transfer via various devices

    • 29. 29.Work and heat transfer of various processes

    • 30. 30.Fundamentals of II law

    • 31. 31.Kelvin Planks statement

    • 32. 32.Clausius statement

    • 33. 33.Carnot cycle

    • 34. 34.Reverse carnot cycle

    • 35. 35.NUMERICAL on II law

    • 36. 36.The order of randomness

    • 37. 37.Clausius theorem

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About This Class

During my college times. I often found my classmates having trouble with Thermodynamics. Many of them even had backlogs when they have cleared other tough subjects like Dynamics Of Machine, Machine Design etc;. However this subject always amused me. The vastness of this subject is what makes it tough in the first place.

My effort in this course is to simplify the topics in the most suitable way possible. I have divided the topics in very small small bites because I think to eat the whole thing would lead to indigestion :).

"Nothing in life is certain except death, taxes and the second law of thermodynamics."

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1. 01.Thermodynamic System: Hello, everyone. In this lecture, we are going to understand about the thermodynamic system and its approach. Thermodynamic system is define us quantity off meta order reason in space on which is studies focused. That means if you're talking about quantity, off matter, we're going to understand it in terms off control musk. And when we're talking about a reason in the space in that regard, if you're going to understand with friends off control volume, the system approach has two approaches, one is controlled mass and another one is controlled for you in control mass approach. We're going to consider mask and in control volume of growth. We are going to disregard Moss. So let's understand them. One by one first is controlling Maher system and another one is gonna call volume system when we are talking about control Maher system yet taking to consideration a system which is having a finite mass. But when we're talking about a control volume system were considering our control volume in which masses disregarded at Miss days no focused on quantity on a particular reason is selected in which the study is going on. As you can see here, the dotted lines represents the control volume surface and promote dynamic systems are off three types when it's closed, Second Money's open and 3rd 1 is isolated. Let's understand them one by one in a closed system, we're basically dealing better controlled must system. All right, compliments is. And that means we're having a system which is having a mass as well as a finite for you. And we're constructing a system laundry because having no thickness, that Mr Volume of the bond itself is Jiro and everything else except system that in the surrounding it is basically, Let's say, for example, if you're considering System Murphy, I seem general means of these two insulin. The arrangement without exhausting our intake fall right So that particular system would be considered as they controlled my system as well s a closed system in that particular system . What we're having is that their particular system is the closest, Um and the whole surrounding that mean the whole June iwas would be at us. The surrounding this boundary can be fixed, are moving the bonding that help assume that is having no thickness. It can be fixed ongoing. Us as I told you, like the distant and selected arrangement in which then, when the piston is going to TDC and then coming back to BGC so that particular idea that particular reason can be considered as a system foundry. No hospitals, the closest on this concern, were considering a piston insulin management again with mass fees but having no exhaust wall control. Mont. System is eventually a closed system here, an anti inflection. It is possible, but there is no mass interaction because the masses finite march is not going to change. Ness is your control warning system. Ah, controlling system is basically open system in which the mass interaction, as well as the energy interaction is possible. And then we have isolated system in isolated system, not even the mass as well as the and the destruction is possible. That means mass cannot come in or go out as well as energy cannot come in on gold. So the very basic example off isolated system would be a Thomas in which we put tea, coffee or even water toe make it remain its heart or cold, so that particular system can be considered as a isolated system. No, let's understand about the open system in brief today. Let's take example off a compressor that we deal with the many power plants and other industries in this particular complaint. Sir, Masses coming in and as well as going out. And for that, we need to have some work done. I won't say, But then is also required. So that means our energies also coming in. And and she is also going out. So what we're considering for this particular compressor, the body off the compressor is considered us the control folio, which is having a fixed identity. So we have understood about the types of thermodynamics systems closed, open and isolated. And we also understood about that system approaches that is controlled mass and control volume. Thank you. 2. 02.Thermodynamic Processes: welcome everyone in this lecture, we're going to understand about property of system and processes as well as straight off system. So basically, what is a straight up system? Let's say, for example, it's a strong is having pressure People density Rho one volume beban and temperature Stephen and another state is what pressure Pito dance till goto willingly, too intimidated. So if there's a changing state, state is work. I didn't defecation office system. So if there's a changing state, we can say that ah, particular process has happened. So from going from point wanted, once you can see here is a change of state and that genuine status following a particle apart initial toe final. So basically this other properties up system. There's a property system from getting from one place to another. Let's say, for example, when we're starting over engineering. We had gesture bustled from 12 and when we complete our engineering via basically the guided US engineer, so that is a part that we have followed the eight semesters. The food here suggests that we follow that eventually leaders from become a engineer, so that is the path and the process in wall in which we have given lots of examination practical five US and many a strike, illegal activities and the final destination waas our graduation. So that's the pot. And these opposes in world sending was with more than any so this particular process that thermodynamic processes basically a continuous change off state. That means from one state to another to another to another until we reached the cool. So this thermodynamic closes is off food types. One is reversible and another one. Is it possible reversible? That means something that can be used at every possible witness that cannot be divorced. So let's understand that he washable process. First, the divisible processes. Let's say, for example, from point for toe. If you're going from 0.0.1 toe and you're reaching again from 2 to 1 for loving the same part, then that particle process can be considered as a reversible process. It's a very slow process, and all the intermittent points are equilibrium. Hypothetically, there is no loss that is required to have a possible process, and it is a benchmarking thermodynamic analysis to study the real process. There's are irreversible process doesn't follows the same part from reaching 0.1 toe Then again, put the one you had to follow different part. So that kind of project is regarded as a either possible process when reaching from initial to final points. There are many intimidated points, so basically we make imaginary line tojoin the initial and the final point, and we considered it a supposes. It it doesn't I mean that it contains all the terminate point, but it's just a mess. Lady line. I'll just understand about thermodynamic property. This type of thermodynamic property one is in dancing, which is independent off mass like pressure and temperature. They're not dependent on Mass, and another one is extensive. We just completely dependent on Mars like volume in energy. But how would this invents you? Property are independent off mosque. How come? Let's understand. Let's in the left hand side when we talk about the pressure. Precious work force per unit volume right? But is it dependent upon must know it's not is depended upon in the molecule forces. Let's say, for example, we're having a ball on which lords of molecules colliding and they are colliding with each other as well. So what we take, we dig basically average off the forces that is the monocle forcing that is applied by the molecules to the ball right, and we take the denominator as the area that gives the pressure. So is it dependent about must know? It's not depending upon the mass, depending among the in the market forces not take another example. Temperature in pledges also intrinsic property. Let's say a mosque and which is heated to a temperature toe. Wanted any senses. All a. Slice it in gloves First heart is having, and by Domas lets the M E and M B is also and by two months, but the temperature in the boat will be 20. Do you sense is still like this? Temperature is also intrinsic property. Now let's talk about space. If IQ property specific property is basically the expense you properties unit must, just like volume per unit mass will give you specific volume. That will be your intrinsic property. Volume per unit mass would be cool, and two cubic meter par K G. That is quite was specially volume. It's in fancy property. No, let's understand about fees, faces quantity off matter, remaining homogeneous throughout in chemical composition as well as fiscal a structure Let's say, for example, you are boiling water or it water. Ben's getting Boyd at a certain point. It feels vaporize. It will convert into still. So what will happen? The molecule of farmland they can conform off water is what edged tool that is remaining same throughout at the in the liquid face on in the gaseous phase. So basically, how many phases are there? So I lied in liquid and guesses. So when you hear of boiling water, you're having both the physics solid history liquid as well as VIP office. That was the guest. Yes, please. So such kind off deviation would be the Gardiner, some multi phase or had a genius. If you're having only water, you're not boiling it. It's just standing there than that particular face would be regarded as a homogeneous place on a single office. And the more edifice the best example would be the stick Ice cube. And this. Put it on a warning. Ben, what will happen? The ice that solid will initially convert into liquid. And then the liquid vin gonna want interesting. So basically, you're having all the three phases so really wouldn't guess, for it's a multi visits Actor genius. No, let's understand about what the static process for that we're going to understand in regard . Bitter political experiment Let's take a distance Langridge mint without any exhaust wall. So basically we're constructing a closed system and we're going to put the outfit mg off mass m. So the pressure exerted on the piston would be the blue by the idea of the pistol. What we will do if if we suddenly put the weight, the process would be very instantaneous and we cannot make it reversible. You cannot make it prompt. So what we're going to do, we're going toe slice the mass in a number of pieces and leaving gradually Put the Lord on the pistol. So what will happen? The whole process will help a number of intimidate point, not infinite and number off indeterminant states will be there and all this triple being group so we can see a quasi aesthetic closes. It's almost impossible, but not completely because some amount off energy, they still be lost. This is the based off every time with them dynamic processes and this lecture computes but this not Thank you so much. 3. 03.The laws of Thermodynamics: Now let's talk about the laws of thermodynamics. So from the very basic level, if he knows there are four basic laws of trouble dynamics. First law, second law, zero glow and so chronologically if you're seeing the zero claw came after first and second law, but it gives the ailment it gives the mildest rate gives the benchmark for the Ramadan. Any clothes, the clock, unanimous beans, basically with thermal equilibrium. The first Lord deals with conservation of energy, walk an energy and heat transfer and tell P and the concept off internal energy. All these concepts. All this Grenadians we're going to understand in the coming lectures. The second law gives the direction off. Heat through as well isn't probably and the federal gives. Then property began still at absolute temperature and absolute zero temperature, basically. So what is the absolute Gerald impression? We're going to understand until, um, unless we enlist the job. So let's begin with the zero votes that they're not lost is that if three bodies are in equilibrium, let's see, B is the temperature off body and TV's a temperature body B, then body see would also be in the same temperature that Stevie would be will be Cito. It's basically a so temperatures, this one and which is basically our idea off hit content off a body. It relates to the average can and pick energy of the particles. It's absurd. Collects it. For example, if we're considering about the temperature off your body, if we're having a fever that savior, having a fever of 100 to be fed height, what we conclude it's not like we haven't you in one particular part off our body. Our whole body is heated, so basically the cells inside our body there haven't different vibration there having different and bridges, and they're vibrating with the different pregnancy and their colliding with each other as well. So basically, days average, frenetic energy and more. That means that's it. For example, beer, considering a solid having a particular temperature. All the molecules that is present inside solid are colliding with each other and the benefit of the soul itself. So each and every molecule have a proper Kandic energy, and they are getting excited you to heating uneven Cooley. So basically, there would be a hellish kind of energy off the particulars, often so that relates directly to the temperature. Now, actually, digital is that the richer at is the Paris Ganic and G up the particle becomes completely chill because there is no moments whatsoever are if there is a moment that averages Joe. So this goes without saying that third laws on Lee Belly for crystalline solid because the very definition of because land solid is what the very definition constraints qualities then Robbie offer disclaimed solid Jill and absolute temperature. Absolute Children. Ambridge Physically No, listen, this train about water, Tom can and make gimmes. It's not thermal equilibrium. My words, as I told in the very first lecture that thermodynamics is big. Basically, the study of three is energy and droppin in Colombia, so this equilibrium is not a normal equilibrium. Is that Ahmad enemy Libya? That means they could be mop, mechanical Thoma as well as chemical and nighties, so that considers that thermodynamic equilibrium No, let's understand. Water and property is basically, let's say, for example, we're heading Ice Cube. This is solid. I'm again taking the same example as they took in the only election because it makes it easier to have the same example toe understand Previous concepts. Let's say, for example, we're having eyes. It's a solid, so the molecules are closely back together. There's very a small difference in between each and everyone. Now, if I You did this eyes and it turned out to be water. So what will happen? The molecule will fall apart, will go further from each other. So that means there's a England is in randomness. And if I hate this particle of water, it will convert into water vapor. And there will be a electric moment between the molecules that civil, for example. We're sitting in a class. We are in a solid state because everyone is sitting in their particular benches and they're waiting for the lecture toe. As soon as the lecture is over, everybody will be running out after class because the lectures what they want to roam outside. And as soon as they get outside, they're in a water state. Let's say they're randomness has windows, but not in a ready moment. And as soon as deal goes out off the periphery of the college itself or the institute where they're studying, they will have erratic movement. They will have their bikes, they will go from one place to another. Some Catholic populism. Some will go to meet his friends, his fellows anything. So that's that were set in motion. So in drop D is basically the art it off. Condoms. Thank you so much. 4. 04.Work transfer: No, let's understand about the concept off work transfer. Then we hear the word work. The very basic definition comes into our mind that force into displacement, but that is basically the definition off. A medical book in rage objectives displaced from one pushing toe. Another Vittel working force on the work is given by W School toe Effin today, where these the displacement and this is what a mechanical bookies. But when we are dealing with the thermodynamic work, the definition is quite analogous but different. And guess what? Thermodynamics instead of the object we're having a system that thermodynamic system. So how to understand if what transfer is taking place in a thermodynamic system? See, I told you earlier that a system boundary differentiates a system from the sounding and surrounding is the whole universe itself. So if there's any change in the system laundry, then we can see that some work transfer has been awkward. In this particular system, it can be contraction or expansion doesn't matter. But if the boundary the system boundary is changing, then we can conclude that work transferred has taken Please. Now let's take example off in Northern here. Let's assume a flute is flowing from one end to another. That's a from 10.12 point four, and I have bifurcated the nozzle into four parts into visited T parts, having different boundaries that is generated by this imaginary line. So if our flu this morning from 0.1 toe, then 2 to 3, then three toe for what is happening, the boundary of the system, if you're considering the this particular benefit of the nozzle at the system, the boundary of the system, if it's getting changed, then we should have some work done. But that's not that keys work is crossing boundary are we can see the boundary keeps on changing, although the vote done, the voke transfer is gentle because we're not getting anything out off it, because work is what is a form of energy. So this particular scenario would be regarded as a free expansion so we can conclude that if the contruction or expansion off system generates work, we can say that the work transfer took place and more accurately, if work is changing laundry that it can be said that work transfer is happening. However, this too is also not true. All this just like in case off nausea. Now let's understand about the Devi book. Or, to be more precise, we d. We work for it closed system because for open systems completely different that we're going to understand in the coming lectures. Let's assume a distance. Lindell arrangement the same one without any exhaust work. Let's say you're applying a force f so the system and the system is being displaced by your small displacement. Let's in deal. So what will happen? The guest that is, are the ear particles or anything that is contained inside the cylinder. It will try to resist this moment so there would be a definitely will be a reaction force against off F. So let's take it does on. So it's part us eclipse, You miss concern. Then there will be a point when way have toe applies some additional force toe work. Um, the reaction at that point equilibrium will be reached. That means the reaction force will be quinto the force applied obstacle to F for the clue. Beom submission off f. It's called a job that will give us our minus f school to Jiro. No, at this particular instance, let be with the pressure off the molecules present inside the cylinder because we know pressure is what normal force but unit area and here, normal forces What are R B e would be your pressure are are to be equal to be into it. Now let's find out the Mecca nickel work here worked in his work force into displacement. So if you're considering for this is small element Oh, off this a small, elemental instance. Basically, they're the crystal has been displaced by a small displacement off deal. Have you had DW school to happen to deal an f It's war, the reaction force itself. That means being to deal and a into deal would be what you're well, you. So this gives us DW school bbv this the walk transfer And if you want Oh, no, the total walk transport off the system then we have to integrate it because we are initially were trying to comprehend it with elemental instance. So integration off VW's called integration off the TV. Now let's make a TV diagram, which is the very important concept ing Ramadani makes when you make a baby diagram from 0.1 toe do here. The change in volume is we want to be, too in changing pressure ISP even to veto because we're taking initial and final. We're not taking a elemental instance. But if we take a elemental strip in this baby diagram off, let's say Dini us. But as the XXY suspect. But it's thin volume axis is concerned, Then the integration off BBV would be the world. Time back would be Quillin toe the area off the read item for the process. Or we can say the area under PV diagram gives the work. Thank you so much seeming the next lecture. 5. 05.Sign convention of work: Now let's understand about the sign convention off booked. So from the very basic designation that we learn from our school times, water on the system has taken its negative involved and by the system has taken a sponsored you. This is what we're learn us. But as the mechanical work was concerned, that means if upset this morning on its one, it's providing work, then stick and it's supposed to. And if we are pushing, are pulling our object, we are doing work on it. So that's the definition off. Does the busy definition of sign convention for a mechanical? But in case of Ramadan is, as I told earlier also here, we don't consider the observation considered a system and the surrounding and the Vogue done is with respect to the change of laundry off the system. So System Boundary provides the basic definition on sign convention in case off Borden in a thermodynamic system. So Intermoda mimics. Also, the wagon on the system is negative as well as the world, and by the system, it's positive, so positive walk done can be considered as a expansion work. That means if the system boundary is expending being getting a book out of it. That's a, for example, in case off, dull by what is the window minus of basically a mechanical device, which you can see in many about blondes what it does. Basically, what it does is some condensed such a that this team is there what it does. Is it expense that steam? And due to that expansion, McNichol work is done and that McNicol work, who tasted their mind and you do this super declare article emotion. That generator works and began the electricity work. It's also far energy, so basically, we're getting something out of it. If you're getting something out, if you're putting your efforts and you're getting something out, then it would be the work done by you upon the system. But if something used you automatically, you just my arrangement. Then what is done by the system Getting my point? Let's say, let's take example of compressor in case or compressor. The system has been compressed, and we have to do some additional vogue do so It's a, for example, for feeling about tires. You can see the air compressors on the adding small the police and tell us So what happens there or even get a just also but generally being a Indian person. We tend to fill our air in our bikes in our cards from roadside vendors. So they are having generally some low grade air compressors but from that bus, but to also they're providing additional walk to it, then only our here is filled in the tires. So that is foot work is being done on the system. So for the conclusion we can see if the system boundaries expending work is done by the system. It is taken as positive and if the system under is shrinking, work is done on the system and it is taken us negative. Thank you so much. 6. 06.Work as a path function: welcome here. You know, in this lecture we're going to defend how work is a bad Foshan. And what was the part? Basically the means to reach the routes, the days that you reach your destination that that was the part. So let's say, for example, leave ever asking your hands in V cheer to carry a load off five kg from one place to another place. There are two routes for the same. The first group is going to take some 5 to 10 minutes. It's a shorter one and the second route is going to take some 10 to 20 minutes, which is a longer. Either way you're reaching your destination, either religion to the next point, the wind fear you want to unload the Lord your carry. But in both the cases, timing's different and land is also different. That means from the first route you had to carry the load for only 5 to 10 minutes. Statements Walden by you for this particular boat is lesser as compared to the work done are the labour that he had to do for the second route in which 20 to 30 minutes or something was there so that bus. What bark is basically if but is different. The Walden is different. Same thing goes with thermodynamic work as well. So let's understand it. In brief, let's say v Hell, two states stood one and two in a straight one were heavy and APIs even impression we even volume. And that s Steptoe. We're helping people pressure and we two for you and this is the baby diagram for brewing. How work is a part function. Let's designate the proposal color but the impossible part as party and the red clip about a spot be the initial and final destination still the same. But the part has been different. Holistic some small strips in both the parts. But it's basically BV for Part B and TV Dash for pop and the corresponding pressure for the same US be dish and be no. The work done by but be will begin by integration of PDV, considering it's a siglo system, right? And the blue A that is the work done by but e will be daily under the same that would be given by integration of traditional TV dish. That means it clearly stating that the doctor, for the different part for the same nation and find the pollution is if friend. And that concludes that work is basically apart from Janet, dependent upon the part that followed. Thank you so much. 7. 07.PdV work for various reversible processes: we have already established what BBB book waas and it is really for only close system entry was simple processes. So let's understand. First water thermodynamic reversible processes. How many type of processes are first is constant pressure purposes that is also called us. I saw Barrick, in which pressure remains constant. Second is constantly renewed pressure or I so cooling in which war impediments constant 3rd 1 is constant, them Bridger process arise with thermal temperature being constant and then we have a bullet tropic process and our idea. Betty cruises in in idiomatic process. Hit transfer two minutes, General and we will nurse turned the bullet dropping processes were no legs established. The PDV work for each and every processes one by one. Let's start with the I Subotic or the constant pressure process for that were made a baby diagram from 0.1 toe pressure being constant but volume, diligent, given and veto. So people is it's going to be truthful to be. It's going toe constant. So for a broad system, see on this process, we're taking posession for open system. There's a completely different story and we will get to it in the coming lectures so w would be given by integration. Off PDV limits would be what initial to final initial wasn't even and Panelists, so it would simply give us p integration. We want to be to TV. Definitely was b v tu minus fever. This is the world done in case off the ice nobody process Next we have constant volume process are I saw cooling process in case I saw calling process Volume is constant You can see in the TV Didymus Well, while you miss constant pressure is changing but it's changing from we want to Peter. So if the volume is constant, that means differentiation off him that Miss Devi would Pajero This is the basic form laughing the differentiation. So when we are trying to find out, vote on mathematically that its integration pdv that will be also called digital. This signifies that the area under the BB diagram is Gino. But pride it, Dad, it's a close sister. Next is the PDB work for constant temperature process are I saw thermal process Prior to that, we need to know the characteristic gas accretion in order to get the voter btv work done in case of Ai Stammel process. See the cat tested gas aggression Basic The body unit gas A question is PVS will do rt Image is the statistic. Guess constant We just given by I'm not by you there The value of our not is given us our heart is kun by 8.31 for Kal Usual But Katie more and use what used I don't make myself the guest but that means the value off get distinct Guest cross plan can be find out by dividing It meant Freeman for Katie, but a luxury marketing home with the atomic mask the guests And for I saw Tom a process we help give he school to Constant since he is gone standard Mr We are also having at the constant from cactus aghast equation We get previous called to constant That means even even would be cool Do people feet or we can also see that BB at any point Let's see we're taking a strip off volume V act at a particular point and pressure p so PV would be cool. And to be one the one that is called topi tomato so we can conclude that be school group you envy even by V. So putting the value in the form lack the blue school do integration p D v v m Indication even to Reto. Because the initial and the final points I've even envy to respectfully so integration even Toby to people even by v tv. So solving the same vol even even locked with a B C or Ellen Reto by the one as the Jadeveon work for that so timely process Also, we know that even municipal topi to Mito That means we to buy beaver can Britain has begun Pepito So the work done the CTV building a settlement process can be all screwed in us people. Demon Ellen People by Peter Now let's understand how to find out that pdv bug in case off it literally possess same case off polito pick crosses The process follows a question that is TV to power and is full do casting on the value off an varies from zero to infinity. It can be greater than goes to Jiro and left Nicole to infinity. Similarly, in the earlier case, just like the idea case, I suitable process again we're going toe perform the same process, even even tow bar any school topi to which power and that is equal to P veto power and at any particular point so that will give us peace. Could do even. We went to power and upon veto power, putting the value off be in the question w school to integration off pdv were the police called tow integration even to be do people even to borrow end upon beautiful and TV solving? Does it mean gives us the Blue Square poop? Even even minus B told me to abound and minus one. This is the PDB worked for a poly tropic process? No, for in case off, a diabetic closes the value of Amgen just comma. And what is Gamma Gamma is basically CP by See me that we're going to understanding the current lectures and the value of camera is 1.4. So the believe in work in case off a diabetic process would be people of, um, minus people me to open comma minus one and the question that everybody process follows his TV to program a school to Boston Now to understand about the idea Batic process. Let's take example off it Business lender arrangement the same example I'm taking again. But in this case, please uh, basic walls because the walls are being replaced by a diabetic falls. That means he cannot cross the system Barbary That is the basic definition of a diabetic process. You musical to Jato right here Got my school to one point foreign school toe. And there's only one more about portion that means the walk transfer takes place from that particular mobile portion out the pistol that miss welcome space, not chill here. But if he fix all the sights, that means if you make the piston also 80 amending, then what will happen? Que bill digital and w will be also Gino broke transfer and he transfer. Both will become chill in case up all around Fizzy abetted waas So it's a very important Just try to understand of all which prevents thermal interaction is known as a diabetic wall, as you can see in the distance. Elena Regiment and its system in close within. An idiomatic wall is called family insulated system. In case exchange of heat takes place between the system surrounding through the boundary wall. The boundary is called die atomic In case of thermodynamics, a diet terminal wall between two thermodynamic system allows heat transfer but not mass transfer. So that's a definition Titanic. So you must understand What's the differentiation between a diabetic balls and diatonic falls? A diabetic force. It cannot cross the system and diatonic walls must transfer cannot be done. So, in a nutshell, we can see the PDV work off passing pressure process will begin by the blues Kowtow BB minus fever for a constant volume. Purcell what says w would be called geo for parts in temperature process doubly school Do people, even Alan to buy even that is also equal to people even Ellen, even baby toe for Polly Tropic process we have double is will be even even minus speak to me to account and minus one for the respect to equation PV for any school monster for a diabetic reversible process, right, because we're talking about us will process to know right? And a closed system w score to people even my last. But we took on the government minus one. They're gonna square to see Depay CVS Good one for one. So these are b deep, evoke forward, impossible to thermodynamic processes in a closest Thank you so much 8. 08.Polytropic index n: they're for God to discuss about a very important topic is the Wallet Property Index. So let's derive it in this particular lecture. And this particle lecture will be completely confined within the borders off cropping index and see a value Tropic process was what BV depart Any school too concerned that I told you earlier. Also, all we can write B one b 12 part and it's going to be doing to the power. Let's assume this particular pornographic processes initially initiating from 120.1 and then and then appoint ascendancy in the PV diagram. What we have to dry. You ever drive those from lower basically the value off and the whole trophic index and how it differs for different kind off processes. So in the basic equation that this people we went pardon, it's called Tokyo into the bar. And if you take la Trobe is ive both the sites we have Allen, even we want to part anise will do Ellen between power. It implies that Alan P. One plus Ellen, we want to bar and school toe lmp two plus Alan b total power. And by so because simple logarithmic form ladies, that means If you're having multiplication inside a law, it can't converting. Do Anisha separately. Modification is there, right? Simple, simple log. Then it implies that looked at the Busan even school do and look to the base e even school do LMP two plus and Alan Embree two similarly a Prior to this lecture, it's my recommendation you need to understand some longer it make formless right So you can just go back to your, uh, school times, notebooks, school times, textbooks and you can find this formless recently there. Right, So after we completely elaborate all these creations, we finally get the value of and us and then even might be true by gallantry to buy fever. So the value of an the sites between minus infinity to plus infinity the value of and for a somatic process is geo fry so quick its infinitely. For I saw Truman, it is one and for every possible area, but it causes it's going to come a 1.41 So basically, these values off and can be easily correlated with the polito big processing question that this building apart and school to construct. So I will give you just from one simple example for sobering process and you can delight for all other processes the value of so far I saw body process What feel pressure school to constant as simple as that. So the pressure is constant, then the value of and should be bought Jiro right Be veto power Jiro School Toe Constant then only be deported over bqool into one and being will be equal and took constant. Similarly, you can die the values off and the porter Big index for all the other cases, like a so called regards to Tom Landry Possible idiomatic. So I will leave it up to you And most probably I'm going to make a separate assignment for the same. All right, think of village. 9. 09.Heat transfer: welcome everyone in this lecture, we're going to understand about hate more so heat transfer as well. It's specific heat, so let's begin. So what is heat? The basic definition off. It would be a form of energy. This is transferred between two bodies on a system and surrounding by virtue off temperature difference. He'd is a transient Phenomena like their study tip us, but it's a work transfer Waas concerned. What transfer waas All so dependent upon system Bondi Asperger's. The boundary of the system was changing. According accordingly, you can say they will transfer of us begin please. But it was not on this room, just like in gets off free expansion case of Nazem. This were covered in our players lectures So similarly. Heat transfer also depends upon system country if there's a temperature difference between the system and the surrounding, and this difference can be calculated on the business. A system Margaret's Mxnet Eban tree itself. But it can be calculated if two bodies are interacting on the transfer off them. Preacher, that means he transfer is sticking place if they just emigrated. Defense days. A hate transfer, definitely now, just like in gets off book transfer. He transfer also has a sign convention. If he did so removed from the system, it is dig anus negative. And if he was added to the system, it's taken us what to do in case a work transfer. What was the sign? Convention? If they're getting a work out off the system that it is considered as a positive and if we have to do work on the system, it can be taken us negative. So he removed negative, he'd added Positive. So that's the same convention off heat transfer. Now let's understand the basic stories off Regina feed. This not turned. It's not very much important, but you must know the stories. So they are basically go through this kind victory of gases and second is calorie victory. So the contradictory of gases is similar to the purity that implies for harmonically bria Marsellus for defining a pressure that means the inter monocle forces the interaction between them as well as if they're striking to a surface. All this concept in the kind of Terry of gases and calorie victory was a really important Tilly in the earlier times. It has been scrapped for a very long time, but the gallery fifth story has find the concept off saturated Weber at such a ridiculous quit. If you want to understand about color victory, you can just google it and it will be in front of you. But it's not in their scope off this particular course, right, But you can. Out of curiosity, you can. This going see? No, let's understand about the moors off heat transfer. There are the three basic morsel transferred that Villa studied from our very basic classes . 1910 plants is we must just reading about them conduction conviction on radiation. So let's understand about them one by one. 1st 1 is the conduction conduction glass. A media. It happens mostly in solid, but it is a very common misconception about conduction. Convection is that people think that conduction August Onley in solid No, it occurs mostly in sorry. It occurs in liquid as well, but mostly because in Saudi and same people conviction, people think that conviction have plans for link been only, but it happens in case of solid liquid as well as guests. But the intensity divorce So we're talking about conduction for so let's finish it then we will go forward to conviction. Let's say, for example, here you can see one particular piece of mental Arby's off material. Something is there. Alright and I'm giving it a hit off cue from one particular end. So what will happen? The lettuce, the lettuce off any any solid body is having a lettuce. The crystal act is that you must have studying your engineering materials like the bravest . Likely says the FCC businesses, such a recipe structure. All this that ever like this. All right, so those kind off lettis will have a vibration. Well, the vibration of the most at the point off contact were hit husband supplied and it feel vibrate. And it will propagate tinder very and because he'd transfer from high temperature, body do load and richer. So this is what conduction. Now let's understand what conviction is conviction expressing different mediums here Medium Sorry bread. Not my word in connection a single media must required, but in case of conviction, mediums are bad because it's a 100 that means for connection toe big please, huh? Interfaces required, like say, for example, solid, then interface, then literate than in the first. Then guess and Now let's understand about radiation in case of radiation. Medium is not at all declared anybody who's temperatures abo absolute you. It will omit thermal relation. Let's take a very simple example. If you're having a feel, all right. Ah, buzzer standing next to you will sense it. Even. See my friend, you're burning up. I think your money. I think you should check your temperature so that is through thermal radiation. If if it them. If the temperature off a particular body in Prizzi's infant that idiot, it will try to escaping every location off the surface. 80 off the particle body, each and every point. It's not pointed one direction. Let's. For example, if you're having temperature off under the bigger the feather night, it will not be planted in your head. It will be. It will appointed Bulger from each in every part of your body that is exposed to air and the part of body that is not exposed. Teoh will get sweaty. Same thing happens for tomorrow, returning all the materials on that note. Let's understand one really unions concept. Let's say we're having two bodies A and B. Both are radiating and giving the heat you A and you be outwards. So we are dealing here with thermal radiation. Okay. Hey, transfer is a different concept. Thermal radiation radiating slid, eating right. So what would happen? That tendency is what? From high temperature to Lord Ambuja, He feels so. Let's see. The temperature of body is greater than the body. So what will happen? Heat will transfer from it to be so let's take you A B will be there. Range. But since thermal radiation has such a tendency that it radiates in on the direction, it's not unit additional. So we can conclude that some heat would be transferred from B two years with getting my point. But the net heat would be all this from higher to lower. That's the basic concept. But it defies the second law. Modern innings. He says that he transfers from Onley from haemorrhage included. But in case off the modernization, when we're considering timer radiation in that case, heat transfer radiation transfer can take place from Lord and Richard to high temperature. It's a bidding what in concert. So just trying to remember now let's define if the heat is a part function or not, is definitely about function, just like book energies also function in case off what? Transfer what Feed it. If we took a PB diagram and we don't do different parts, explain how work is a back function. Something can be done here in case off transparency. But here, beer to take a ds diagram that this temperature on drop it, agra and why you're doing so when we're going to deal about clauses, inequality and all. Then you can understand it properly. Just try to understand that we're taking a B s degree, right? So here the area And just like in case of what, transfer that daily under beauty going against the will Casper here, the area the PSD Island gives you hate. Now, if you can see there are two parts he can be initial and final states are one and two, respectively. So you can clearly see the media under part B is gated in the area in the parking. That means he is also about function. That means you be would be all this good at than you. Now there's a very important concept in turn dynamics. On the basis of the same, we are going to derive many formulas, and we're going to solve many miracles on the same that is specific heat fizz. Think he'd is the amount of feed boy you need Mass required to raise the temperature by one daily Celsius. Specify heat at constant volume is denoted by C V, and it's specific heat at constant pressure. I think there's on the statements. It should be specific heat at constant pressures. It's a little pressure here, but especially heat at constant pressure. It is denoted by C P and for in compressible substances simply becomes equal into CB and for gases. Sippy is greater them city. So let's define both of them. And in the coming lectures, we are going to help. Very brief with the discussion about them, constant pressure and cost in One specific is so specific aided constant pressure, Mr. Defined as the amount of heat by unit mask the black truly stood. The temperature by one degree senses at constant pressure and specific heat. At Constant folder is the amount of heat boy you need Mosque required to raise the temperature by one degree Celsius at Constant for you. Thank you, Sarge. 10. 10.Work apart from PdV: we're already established about the big TV work and derive the formula for very ist thermodynamic possible processes. Now let's understand what a different kind of dogs are far from pdv. Because the scope of the moon enemies is not only limited to PDB book, there are different kind of works as well, which influence it electrical workshop for the ST Ng work feeling. But on even Oberg images stretching of IAC also includes. So let's understand them one by one meaning to just a brief. We don't need a brief knowledge of the same. We just need to have a supervision order so that if something comes up if some internal numerical or in some concept, we won't speak with complaint, so forces electrical work they said nothing must you see here you just need to know that the work done for electrical process would be being too. I, where v is the world s denies the current no shaft work is a warning one because softer corresponds to the power of the transmission shaft and the drive shaft. In automobile sectors, all this corresponds to power transmissions. So what happens in the shop when a Shafter dates powered transmitter some basic definition here. The Vogue done is quite similar to the mag nickel loader in case of mechanical organ. What we had forcing displacement here. The force has been replaced by dog, and this press minutes is simply being blessed by angular displacement. So B is dark, empty days. Angle off tradition are angular displacement. Now, if it take us more degree Operation Dictator so that would be going back Deep Omega by DTV May keister two For the ship that's just stealing work. In order to understand studying work, we need to understand a particular experiment. Here. We're having a visit area Bedzyk for in Closer Inside Breach has more families put and the family's attached to a pulley in the police Internet age with a mass when the mask most pro 0.1 toe do, which is basically a distance off edge that we're taking. What will happen with this arrangement? The fan will start for Didi, but as you know for idiomatic wall, he cannot come in or go out and what transport would not be possible. But what transfer? The natural transfer is possible for the whole system whole arrangement that is here but the work transferred in case off this in closer, in which all the walls the closing walls are idea. Betty Cues. You know, double is Jiro for Think close, but the well done in this case will be going toward the potential energy because the Marcie's moving down. What distance edge, Empty de omega one. Do as I don't really this This is an enclosure which is surrounded by anybody. Walls. So Worley will be Gino because, said close system and we're going to have a good process. So PDV work is general here, and it's the are getting work. Also, protection is also known just like the shaft one. So we have DT tha it's going to empty it. This would be what your network Giannina stealing work Next is a film work film working basically dependent upon surface area and the surface tension. That's it. For example, we're having ah, film off dimension being Toe D. If I want to increase the area by D. A. The vote done that is quite buso begin by integration even toe do Sigmund being their signal Is the surface tension last but not the least? Walden in station away see, just like the thermodynamic walked in the pressure forces volume Magnum. The idea basically the area off the pressure. Worse is volume diagram gives the work done here. If I'm stretching a tin vier for with the Lord, be the wagon in ist rating, this particular wire or bar would be cool into the area off Lord Forces Deformation Magnum , and the work done is given by half being do deal or building. Now let's take a numerical and let's Start will solve it. Ah, mass off gas is compressed in a quasi static process from a piccolo paschal wind one meter cubed to write full makeup. Paschal, Dr Gero Tree, Me Turkey Find the work done. Assuming the process, Toby wanted Toby. So what is given here acquires aesthetic process and initial and final states. Cuban and the process is a Bonnie dropped because well, and what was a quasi static process from the very earlier lectures? Very slow process. Gradual dance to be a possible one, but not so let's on this one. But first what we know that we have to run first. If you're stalling any numerical for straight down what you know and what is given if you don't want inclusion, what you know in the answer you can night inside. But what is yuan is a must. It's manage it right on it. So first in the ocean, Waas returned dead. It was a balmy tropic process. So for a point open process what we had BV to part and it's going to constant and w that is the work done was what people viewing minus p to be to open end minus one. What? What What are the things that was given be one was given a particular Paschal Everyone was 10.1 meter cube beautiful US point for mega Paschal And we do want to point your three middle first of all from the given data trying to understand if the units are same or not. He had one unit was giving me the Paschal so you can convert it into a pillow Paschal, you can little vice versa, but it'll take a lot off effort to do so. So just can wanted to kill Abascal. So be do would become for a nightclub Oscar. Now how very important thing is not given. That is the Poly dropping index and for Polly dropping index. We had a separate lecture, and we derived a formula which Waas locked with the Basie. Alan B one bite, Vito is upon Alan freed by fever. So from this crime lab, by putting the values that is already given the cushion, the value of end value for topic indexes coming up to be a what? 1.336 Now walk down. Begin. Bad people. We want minus Pito group on N minus one. And we have found out right now we'll put all the values and the work done comes up Toby, minus alone by 90 You know, jewelry. So the work done is coming in a negative. That means what we can conclude. Walkies done by the system are on the system. Work is done on the system. Minus means work is done on the system. That means we are doing work on the system. Plus means work is done by the system. Thank you so much. 11. 11.I Law of Thermodynamics: Since we're done with heat and work transfer, let's propagate toe the first law off thermodynamics. The fundamental definition off First Law is energy can neither be created nor be destroyed . It can be already transformed from one form do. It's a very elemental definition that we know from our school days. Now let's understand thermodynamics. First law in terms off you by fucking did this first ease for a closed system undergoing the cycle And second is for a closed system undergoing a process. As far as the open system is concerned, we're going to cover it in our coming legis. The first loft Amada means for a blood system undergoing the cycle get only be understood with the help of experiment. That is the Druze experiment. If you're going to call in this session when we have talked about the world done that, it's different from the PDV book. We came across one steering work, so if you can recall, you can see the same punishment here with slight modification. That means there's a thermometer addressed here in the left hand side above Washington. You can see that, right? No, there's we already know what stealing walkies. We are not going toe Indians with that, but you must be attention that the jewels used Montgomery as the material that is includes inside the idiomatic falls. Now, as soon as the mass M moves downward casually because we took it as a quasi aesthetic process, that means we slice it down into a number of pieces and gradually put the pieces together and you do it so it it's coming down would to look distance off. And what is happening. A bullies relating and the sharp is attached to offend and the sharpest sorting, and the friend is totally inside the engrossed keys. So the finding off Jules Waas What? That how much walk he's giving to desist, how much mechanical work his you do system because the really be work is delivered. This warning was constant. So how much work is Ginter system is directly proportional to the heat transfer. This was the initial finding off jewels, but Jews didn't good likely getting to this conclusion. What you find out initially is dead. The initial and final time preacher off the case, the material inside that is the mockery waas different the final temperature with this particular arrangement was created then the initial temperature and what was the mission from potential temperature was just like that. I made temperature initially, so the change in temperature was brought by boat. It was brought by the technical book as well as the sharp work I don't understand because the mechanical work is equal into sharp focus. Well, because the bully is rotating the shop, I offline is industry. And you do this this kind of work, what is happening? The molecules off the material that is inside the cylinder or basically thing and closer is getting excited and their colliding with teacher and they're gliding with the vaults. Ultimately, the temperature would raise. So the final conclusion off this experiment Waas What did the walk done? Waas badly proportional to the heat transfer use found out with proper position. He found out that what's your amount of world he was putting? He was getting out in terms off heat. But the vice balsa waas not possible that we're going to cover in the coming ledgers. Is it possible to convert all the heat to work? No, it's not possible. All the work can become wanted in to read, But all the heat can not be converted to work. Not until now. Some engineers mid which can convert all the hit work, all the problem. The humanity will be sold. So getting back to this one so we can see that for various Walden and corresponding hate the summation off Ogden would idly coolant directly proportional to some mission off heat van be removed. Its proportionality constant. We get the constant that is called Zurich Relevant are mechanical equivalent off heat. What do you do? Dimensional homogeneity. We dig g us one new commitment. But that means there Walk down network done is equivalent to the net heat output ahead Passport. That means energy is conserved. So what was the fundamental definition off? First loft thermodynamics and educate night would be created. No, we're not creating energy and and cannot be destroyed. No beyond no destroyed any energy. It can be only transformed from one form to another. Yes, then that you transforming from work to heat. No, Let's understand the first law of thermodynamics for a closed system undergoing a process we have already established truths Experiment that the psych lichen trickle off dead tablets called to cycling to go off. So for a proces from 0.4 to 2, we can say that you want to do is call toe double loop one plus tell e What is this deli for? A process? Because it's not the cycle for cycle. We had a different approach and we found a different thing that miss How much heat waas Gender data order getting out of the system. Waas. Do you respect with the work transfer that meets work? Transport was likely proportionate with the heat and the energy Waas conserved there. But he had heard can not be conserved because the process it's a one day. It's not a doing. So what is happening here for this particular system? Some energy will be sporting the system if he is coming inside the system and he out its queen out of the system that we have eaten is greater than he out. Some energy is getting trapped inside the system. This would be the inherent energy off the system, not understand this concept. We need to understand the background off energy. So energy is basically off Buday transient and its border. The transient energy is like he didn't vote in exact dimensions and are part function. They flew from one part to the stored energy, our intern off two times microscope began microscopic in the microscopic level, the it's the energy at molecular level and the example for the same would be internal energy. And in the last light, as you have seen, then e that waas the energy that was stored inside the system. This is what the internal indeed, sir, and for the macroscopic level can intake and energy and the potential energy would fit the profile. Now, if you can recall for the equation that we do for energy for the first law of thermodynamics for closed system undergoing a process, what we had Q. One toe, it's cool to the blue 12 plus tell even tell E. Waas what? The Internet energy. But But there's a big explanation toe the same. Well, the Dell either stolen and you'll be Quinto Ali internal energy that I will be explaining. So just be intention he had E is what that submission off the addition off kinetic energy potential and as Bella's internal energy. But this would be equal in tow. All internal energy Delhi would be Quito Onley in demand energy in case the can etiquette, energy and potential energy is geo. So even when we're fighting eating differential form for the basic question we have accused Dida blue plus B e. This particle equation is very for both open and close system. But then we're talking about a closed system in which parenting energy as well as potential energy both Hachiro in that case we have pick you is goingto be the ruthless deep. You barely use the Internet energy. That is the energy that this does being exported inside the system. Thank you very much. 12. 12.Energy as system property: In the earlier lectures, we established that the Gen trick formula for first lof thermodynamics is what Dick you? It's called o d e plus datable were dick usta. Hey, transferred these. They're not transferring data blues, the doctrines in which the energy has a different story. If the potential and the kind of energy becomes you, the energy remains is what they energy that is stored in the system. And that is what the internal energy. So now, if for a particular system, if the voter is on Li Bt because we have already discussed different kind off not far from PDV, it also. But if a particular system is having is undergoing on the PD fever in that case, this formula will change too, because called poopy Devi Plus do you and by the writing do you the glass in case off a Petri work for the closest Andrea constraining kind thing. And it's important analogy, as do that's why the farm law modifies itself. So Dick use called PDV plus deal in the same question. If you consider that the process is I so Keurig. So in that process, be Cuba becomes be you and what is basically the walk transferring that security process we do. The work is Jiro. That's why Joe would be here and be cool. Be cool into the changing or basic leader intern image. Now let's understand if the energy is a property of system on C in the creation, Thank you. It's going to the people s Dedham Vale V villa. Properly righted the dick you and DWR will exact Defense ship. Why D is the exact differential. So basically those quantities on those and ideas those who are exact differential did can be. It's not always true, but most of the pain are the property of the system. Now let's try to define it like toe bruises I want to do. Is there any Children final on day that three parts E but A, B and C so you would be given by E A changing E a Plus W and Q B would be hewn by that e V plus W B Off you can write you a minus w. It's cooled to minus L. A and the blue BB minus Q B school to minus Tell e B Nawas. That's but our previous examination was concerned as far as the Jews experiment was concerned. Submission of ordnance will do submission off he draws for. All right, So what would happen here? The bloopers, the booby would be calling Took you a plus. Q b our intern. We can say changing energy in part A is equal to minus off changing energy in part B l e a school to minus. Would that be same thing we can do for part C and E. And after combining all these, we get a final question that is, Dell is glued L E v Saluda easy. So what did you sing? The stored energy is a bind function. He transferred in bulk. Transfer us not only and have g that is stored is a blind function and it is a property off the system. Thank you so much. 13. 13.Energy as a system property: in our school days, we came up with a formula. I think during our nine repent the formula was what cues will EMC, Dell Tea And they're sold many miracles, many questions using the same formula. And we used to get Marks also used to get the correct answer. But that was amazing how this formula came into existence. So let's deal with this problem. But first of all, we're going to do it for M C v. Delta, that is, hey, transferred in a constant volume process. As we know. For guesses, CP, that is the specific heat at constant pressure is greater than see me that is specifically that constant. And what does CBC revolves? The hit required to cause a unique change in temperature in a unique quantity or substance at constant volume around the only ledger in the Penis lecture Basically what we established that becue it's square to do you In case off it, I supported process. We are going to make it the base for the same No, from the definition itself, the specific heat could be regarded as dick you By DP. That means it's a function off them preacher inversely proportional. You can see, but it's basically itself for constant. So this is basically a mathematical presentation. So for C B, we would help dick you by DT wit respecto volume And as they were already strapless dick use will do to you that is the internal energy. That means we can like it here. CVS call to Dubai duty or you it's going to see and do did what Internal energy and temperature are the property of system that you have to remember. And if you're having any confusion, you can go to the introduction section and you can find it how thermodynamic properties that defined. Now we're going to integrate both the sides Indication Oneto use called integration oneto seaweed ET because we're taking a process from one toe. So after today, to help you to minus you want school to see Daddy and here we get tell you that is changing . Demonology school Good CD dlt are doing more precise that specific internal energies given by CB Indelible. Now, if you're considering a mass off an kg in that case, tell you we could do am cv del. But as I told earlier as we established earlier for us according process. Thank you. It's quite a day that you d Q. Is going to do you so we can write it here. Q. It's called toe M C v healthy, and that's the problem that we have studied a long time. He transfer in a constant volume poses, Thank you so much. 14. 14.Enthalpy: Let's understand a really important topic off troubled annex that is until be and they'll be basically tenses about the hit contained off any particular system at any particular student. It is denoted by Etch, and this base figure will be that this per unit mass is given by standard by small egx. Basically, in helping is a property off system. It is not in exact defense ship. It is exact difference here. A like heat transfer, invoke transfer and they'll be is altogether doomed by the Metical from LA Etch is going to capitalize school to you plus BV. Their PV is a floor work. It's not BBV work. It's a baby boxer for work. It's a different kind off book. Among small edge or space figure will be is given by a small you yes, small piece movie that is a floor. But Katie Now listen, Mr the Heat transfer for Isil Batic process just like in case off the ice. So could posses were few established it useful to the U plus pdv So we are going toe extend the same conclusion and we are going toe Get the dessert for as somebody process as well. Now here since we shared this constant. So in the question, Dick, use goingto do you plus PDV with simple differential Formalize what we will get its dick Use Quinto the U plus D off t v. That means big. You would be equal to be off you plus peeling And in the earlier portion of this lecture, we have they used debt Smallish is what specific and helpings going by you plus Beanie So what we can late four i somebody roses we can write that he transfer Did you is school do until b d h all we can say for one kg off substance under going on I so body process in a closed system here transfer is goingto change mental. 15. 15.Heat transfer in isobaric and isothermal process: Now let's understand about specific heat at constant pressure. So basically it's sort It's the heat required because a unit change in temperature in a unit quantity officers spends at the constant pressure denoted by what city So similar kiss . Just like engaged off CB What? We don't use the very family or formula you is going toe M c v Delpy. So like that we're going toe find out a very family from blood that is on CP Delhi. So what is the General form? And Sid lt. See, Was this space figure hit constant for consideration? We have C p for concern Hollow we have seen So let's they use the farm block us goto M c p similar gives here also CPI would be quinto ph upon the that means after integrating both the sites, have you have That s what OCP daddy and for M is the mass transfer in the substance Dallas school toe m psychedelically. And for a blow sister undergoing an automatic process, we have what he was going to m c. P. Just like for a closed system undergoing I socratic process. We had empty without teeth for a pro system undergoing I somebody process, We have m c p dead. Now you understand how the form like you is called am Severity came into existence Moving forward Let's find out that he transfer, You know, I saw German process for I saw terrible process What? We have temperatures constant now for the idea Agus, if we are seeing Idol gas in question PV school constant it's a basically a hyperbolic relation in this case, also, we will imply the same precision for from, uh, 0.12 we can conclude that you can say that you want to school to tell you plus w one toe in a closed system. We're W is what m c v d l b because for this particular process on so temperature would be are basically here transport be goingto Dan, you no tell you Square to Geo because it's s o temple process t zero And for any Isotoner process we get good. He transfer is equal into for transfer. But it doesn't mean that all the heat can con wanting to work because such kind off in Genesis kind off process doesn't exist again. I'm repeating myself If such kind of processes the news to our. It gave him the existence. It will solve all the problems you humanity. But the vice words as possible because as part of the jewels experiment was concerned, all the world can be transferred to heat now so he transfer can be given by the work transferred. Nice optimal process, which has many variants like people given Ellen B two B one or B two b to Ellen we to buy even our people, even an Olympian by beat. Thank you so much. 16. 16.Heat transfer in adiabatic and polytropic process: Now let's understand the heat transfer for a diabetic process. As we all know by now that a diabetic possesses hate transfer doesn't takes place cues school Duccio. So what we have done if we transfer, is not there it. So if you are doing work in this case, what will happen for the formula that we have from first locked of modern innings from a process from 0.1 to 2 Cuban? Don't be tell you. Plus w want to tell you is what changed in two languages. That means you transfers. Nope. Inglis bird work transfer would not be gentle. So here he transfers your acumen. Preschool Pajero that will give us del you That is internal energy plus w want to school to geo on into vacancy Tell us, go to minus off the blue 12 So we can conclude that in case off a diabetic crosses any border on a a diabetic courses on Lee changes you. That is the Internet anedge and hear what is said of the water. Working for a diabetic process. We all know it's people being months between two upon common, This one where gamma is given by city by C p Next is the heat transfer in case off it Polly topic process See, for Polly Tropic Process The Gen req formula is what pivotal part and school do see or constant are there and is the Poly Tropic Index and we're already in over. Earlier lectures were already found Mathematical deduction for Polly Tropic Index. Now, in this case, also what we will go will use the same first lock tomato enemies, Cuban do school do Danu plus w into since this process is undergoing in a closed environment because we're taking us closer because I know you're not dealing it open system that will be dead after the study for energy question. So here what we can see tell you it's quite toe What m c v del de this we already discussed . You can check the only lectures and the work done is given by what beyond even more desperate to do apart and minus one. Now, this is one of a reduction that is CV, that is the specific heat at constant volume. See, Quinto are by that is the statistic gets constant upon column minus So this is a mathematical deduction. I have not covered in the circles. But I might give you it assignment. How? Putting the value off a specific hate at constant volume. What the hell you want to school? I'm CV instead of cvv. Right? You want out upon gamma minus one? Do you do? Ministry one plus B one, B one minus b two e two upon n minus one. This big you b one b one My Let's be. Do we do would become we do we do minus people. Be one upon comma minus one, Faisal, because we know the characteristics. Gas secretion PVS What'll Ahmadi. So I beat that is Artie toe and minus rt. One would be converted into 3 to 3 to minus people even. Obviously, we have comments one plus B one B one minus speak to wait upon and mines not solving further. We get people. People minus between two outside and inside were having in the bracket one upon and minus one minus one upon comma, minus one For the solving the question we get people, be one minus B two B to open and minus one in tow. Gamma minus and upon comma minus one. If you can focus here you'll understand this is nothing but the poly Tropic worked on people. We want my speed we to upon and management is what the Poly Tropic worked on in upload system. So we can say he transferred in. A poly tropic process is a little gamma minus and upon comma minus one into the work done in a poly tropic process Thank you so much. 17. 17.Numerical I law: Now it's solving numerical for first love, Pamela Lemmings. And as I told you in the very introductory lecture as Personal Medical Portion is concern. There's not Muska what in this course, because it will take some what, 60 to 70 like just to cover all the new Nichols for all the portions. So it's 100 guests from my side in order to excel in this particular subject. It was all a lot of medical. You're to re portion is being covered completely. So what is your what your work is to solve us? Must Nicholas you can get, and if you're having any problem, you can ask me in. The question is a section. So let's all this limited force. The ocean goes, a flute is confined in a slender fitted with spring loaded frictionless, Pistone says that the pressure in the flute is a linear function off value given by B school toe. A plus B week at internal energy off the flute is given by you. That isn't closure. School toe 34 plus 3.15 p. Pressure That isn't Globus envy all you partisan me to kill. If the initial state comprise one sounded CLO Pastor Pressure and Point Joe. Three meter que volume and final straight is 400 Club Oscar pressure and point you six meter volume with no other work done that done by the system. Find a direction and magnitude off transfer. So first of all, let's make the arrangement. This is the best insulin duration with no walls, and it is loaded with her spring arrangement. The pressure is wearing with what peas were to a plus B V and A and B are the constants that we have to find out 1st 1st of all, in order to propagate and what this is giving, given the initial straight that it's people 1 70 kilo, Paschal and V, 1.2 meter Kill and Peter for include Paschal and we to find your six meter in. The analogy of the food is also given in a immigration. You scored 34 plus three from 1 45 p. V. So basically we can make a TV diagram here with the initial finance, which is that we're having B one development, which with the one on us where Lester pressure questions also given so you can see that Bebe diagram you right now from the first law, Promote enemies If you want to goto w plus w oneto I'm here to find out. First of all, tell you that is done. Tonality changing. Tell analogy that will be worth final minutes. Initial darkness. You two minutes You on. So putting the values off B and B in the aggression off Internet allergy that is given the question that is 34 plus 3.15 p v. We get you want and you do so all in the same big ente changing turn on energias 59.346 kilo. Now the Bogdan is nothing apart from P D viewer as giving the question direct with no other world done then by the suspicion. So we have worked on a speedy so here he is, very much a plus B B. So we need to find out the value off A and B in this case. So he's also given integration for my April's believing. So we will put people and be two values here and this will you us. After solving a envious minus 60 and seven 667 kilo busker so putting the value for finding out the work. Transfer V. How the lower limit we want. That is Point Joe Tree and upper Limit. We took 0.0.6 integrating We get 8.55 total as the folk so easily we can find out the hate transfer that is given by tell you that we are only found out US 59.346 plus work transferred. That is 815 So finally he transfer is coming up to be 67.896 closure. So since it is in positive, the wagon is coming positive. That means what it is being added to the system. Thank you so much. 18. 18.What is a open system: So as far as we're covered, the first loft mood enemies for close system No, we're going to propagate to the open system. We're going to implement the first law of thermodynamics toe the open system. So what is a open system? Basically, open system has two different endings. He forced powerful allergy can come inside and energy can do and mass can also come inside and mosque and also live. So basically, in case off open system, we are going to deal with a different kind of tendencies. One is mass transfer, another on his energy transfer and the collaboration of both of this and babies. The masters from the energy transfer with Cuba's what we call the study force Energy creation are in short form as f e. Many students have a misconception. That s f e is a completely different pour some thermodynamics. It is not related with first or but it is in fact, the first law off more dynamics that this implied toe open system is what your study for an education is. So sf is nothing but first law of thermodynamics for open systems. Another name off US locked Ramadan mix for open in the last lecture we're going to understand about mass fluid. And after that energy for it and eventually we will be going toe study for energy creation . Graduation. Thank you so much. 19. 19.Mass flow rate: in the last lecture we understood about water. Open system basically means I'm the two different tendencies that is happening now. Open system that is mask and go in and go out and energy can and analogy can live. So the corresponding and tidies that we discover what the mass florid and the energy fluid . So in this lecture, we're going to understand what mass floridis basically so definitional mass load It is what the amount of mass flooring through a section, but you need time. Amount of Mars flowing through a section unit that means mass flowing per second. It can be per minute. Also, it can be pulled out also so by unit pain defines that Matrons think that Mastro did it is a basically posts again. No, it it's not Digits by unit. Time can be minute, second millisecond or even our now to understand the mass floated in the open system. Let's take a example. Offer body blurred system in which are small. Walk it off. Who is there from which of fluids coming out with Velocity V and there would be the bifurcation on this velocity. One would be tracked tangential velocity, and one would be done? No, marvelously, that is a normal or perpendicular to the surface off opening. Basically this know Marbella city is the ballast from by which the flu this coming on perpendicular? No, the mask floor. It would be given by rope into the normal velocity in tow. D A b is the small, elemental area for opening. And here you have to understand this D m. The mosque fluid is also in exact different ship. When we were discussing about the first law of thermodynamics, I told you that apart from energy, the what transfers Phyllis he drives for both were in the exact defense ship that was did. This doesn't contribute to the property of the system. Their basically part function there, depending upon part. So here we can finally conclude that mass floated heat transfer and walk transfer. All these are in exact differential. So it's the mathematical portion that is confirming it's a part function, their part function, and they do not contribute to the property off the system. They depend upon the but so same thing goes for months fluid. It also mass floated also depends Honda. But that is forward. And one more thing for mathematical point off you. The integration from lower upper limit off in exit differential is not possible. That means integration on one toe. Do off. Beat them. It is not possible how he writing in exit different chills, just very light Indian crossing it in the border state. Beat them about it against load. Now if he simply integrate both the sides were integration of being more limits upright Got that's not possible. Square toe integration off robi N. D. So this is your mask loaded onto part Doc. The square toe integration off Robien be a where via Mr Nano velocity is the limiter area, and this is valid for both compressible and in compressible fruits. Now this we and this normal velocity is not always equal. Let's say, for example, you take example off it, you border basically pipe in richer, offload its flowing. Now let's consider a small section the dotted lines that you can see this one section off Prosection idiot D b A customary If you can see here the boundaries bondage the inside ball revolves off the tube are basically the pipe. The velocity of the flu would be Jill because they will have us the Internet said you do the interrupt friction off that Dubah basically fiction party. But they do itself The molecules of the fruit would be guys there. So we will be jiggle in the corners are basically the inside off the inside bundle of the piper. The two on gradually in visited the midpoint and then gradually decreases. So basically we can conclude that the normal velocity is not at all equal. So we're to take average velocity which is owned by one by a integration offi and consequently we can write the master. It is Eun Bi Ro e into average velocity. This is your actual mass floated the fall off actual mass flow street? No, just like conservation of energy. We help conservation off masses with So if some Mosses getting inside off system on some ass is going outside the mass getting inside is greater than the mass doing out there just in case of energy as well. We had what internal energy, The energy that has mean stored in the system. Same thing happening here Also in that piece of conservation of mass, the Moscow inside off the system is no equal to the mass going out of the system. Basically, some matters doing just I told just a while ago that some molecules off the flute is getting sticked to the walls, the inner walls, the inner boundary walls off the pipe. That means some mosque has been stored inside the system. If you're considering this particular Piper's the system, let me use em coming in minus m going out his word. The energy basically Mars is stored in the system. We can ledgett us, Della and for a timed it weaken right and in dot manis I'm out daughters called d M one fleet down where detail is the time interval for which for being the input and output off the mass is taking place. Now we're coming to the main point. Steady full forest. Any flu volume will not change over the course off time. The details that we're taking more while we will not change at all. That means B M. Upon deep down is Jill, that is, masses consult and a constant mass fluid there that Miss M in become will do. I am out. It is not practically possible, but it's a too organized and baby. That means we can night from the elbow Farmland that feel found that is I'm not a sculptor . Roe v average pickle Right row A 131 school to grow It will be This is nothing but the continued aggression Just like him fluid mechanics were You can't meet your question. Maybe it would be one is called Tito. Similarly, he'll be help Roy, When everyone is going toe to toe, this road will get cancel out and we have only one is called to it Just like foot mechanics in the next lecture will cover the energy transfer. Regard the energy busy. Thank you so much. 20. 20.Energy flow rate: so in the last lecture were covered about the mass florid as well as the energy. Florid No, it's interesting what a flu work is. Basically, let's say, for example, I'm having a bip in which afloat is flowing, all right, and I'm taking this month elemental strip off the fruit. So in orderto get this elemental food from one place to another, let's go to a distant and a walk has to meet him. It can be I did on the system by the system. So basically, this flow off this elemental stream from one place to another. Here, in this case, is the district's end is what the floor work is basically. So it is basically what, just like the mag, nickel bottom falls in displacement self So if he considered B as the pressure that is exerted on this elemental strip and is the idea that this perpendicular toe this applied pressure, then what? Fear be into a into a pen? So basically the floor work is nothing but be in movie. This is the work that is the quiet human dender flu does the basic definition off floor work. No, Initially we understood that engages off first law thermodynamics. What he had walked runs for plus internal energy are basically energy School, Do what you transfer and they're already understood. Why are Jews experiment? That all the work and we can want any doing if you transfer But the wise wasa was not possible. So combining both the things v understand that total energy is what a combination off internal energy kind, antic energy in potential energy In the earlier cases, when we were sold in the new miracles, when we were doing the jewels experiment and when we were finding about the heat transferring various processes we neglected this can taken conventionality. But in this case in its steady through an education are basically for our first law of thermodynamics for open system, we're going toe include them. So the total energy is Internet energy blast kind. Take energy price potential energy. That means you plus half MV squared plus mg Jed. So if this is total energy and I'm dividing it by em so it will become what specific total energy, It will be denoted by a small e that is given by U plus. We square by do plus G jet. Now let's understand about an anti billions, just like NGS off musk food it Glenda event me a blind, the conservation off months. What we did. We got the mass inside and got the mass outside and some mass was remaining, said the system and that mass. Osborne's time intervals concern Waas Eun Bi Diem by Dido Dita was the time interval, and that was equaling zero in case off a steady flow. But it it's not practically possible. It is only a theoretical deduction. Why not? Because, let's say we're taking on in the same example off a pipe, some molecules off the flu that is flowing inside with that boots in a boundary in our boundary wall, basically. So it is not practically possible toe havoc complete study for, but it can tend to something for energy balance. Also, Egin minus E out is given by Dell. Eat. That is the energy I could militate in the control volume. Alice Quincy. We have taken a control volume here, and we can write that e in. That is the alleged that is going inside. It's definitely bigger than the energy going outside because some energy's been installed as the internal energy now E in minus e out would be given by D E by detail. Just like just comfortable with the case off Mass Pellens Now for Australia. Awful. What? Fear del e g or biggie by Ditto for baseball to Jiro or energy that is coming in should be willing to energy that is going out. So knowing all these things now we can derive the study for energy Question in the next lecture. Thank you so much. 21. 21.SFEE derivation: welcome everyone Before driving the study of energy Christian. Let's understand its basic definition. The study for Energy Christian, which is also denoted by S F w E it's used for open system to dead amended toe get energy. It is assumed that the mass floor through the system is constant. And it is also assume that the total energy input to the system is called with a total energy, just like ville understood in the previous lecture, just election before this one MAS floated and energy food it and accordingly read it What mass balance, conservation must and energy balance That means must in school to mass out and energy in this court to energy l That was the conditions for the study from So this is what the basic definition of study flow. Energy question No, we're going to drive it for that same. We're going to take arrangement in which input wall is their and our football as well as a drive sharpest there because in this case, we need to understand about to kind off work. One is a external work because what is the output were getting off the complete floor off the flute and 2nd 1 is your floor work that is done by the food we have understood What floor? Waas in the Pierce video That trust jobless will be now in this arrangement If you can see there are certain and I desert in here First off or we will go through each one off them one by one for truffle dick You bite details return That is the hate transform And one Not that Waas that is the must florid in the inlet in m two dot is a mass floated a doubt lead be one v. Even this way is returning small letters. So try it on the census specific volume, right, Because if they're taking mass florid how can we take the emotional volume? We have to take the specific volume and respectively we had to take specific total energy Also specific energy also so even right and will not be one small We won any small. Even that is the localize condition in the inlet and similarly for our outlet. And do not we do in tow and it And if you can see there is a difference off height from the dead, um in the importance will also put Jed one and checked. So these are all of the things now if we can. We're concerning this system. Let's say I'm going to take a small mass element that in lead that is given by D. M one and elemental Mass at the exit or the exit fall or the output fall What, so you can call off? Must demand No big you buy Ditto is the He would transfer and beat the blue by Tito is the look transform Basically the book we're getting out off shoved The musical is a shop for and B even Beavan Mr. Flow, what body unit must that means? Let us try to understand. See here Beaven V. One that is really is in swallowing plea to veto this small That means we're having specific volume. So this people v even would be flow work. But a unit must try to understand because this V is not capitals is small. We're taking a specific calling because why we are taking specific about him Because we are taking the mask floated We were not taking exactly the mass right And the same things for why we're digging small e why? Why were on taking the capitally because we are taking specific total energy and the reason me and this same is the previous one. That means we're taking the mass flow rate. So if the one we won here is the floor work body unit mosque that means find outflow. What were to multiply it with Mars itself must flow rate itself so it would become so what would be Quinto and one, not even we even and the floor work And out uh, exit or the output would be and do not be. Don't be too no, We know the Ekstrom external work is there, right? Some shaft work is there. So let's consider this sharp for us. W x and the total look transfers double now what we have We have a floor work in the elect at this people we want someone. But if you're taking the elemental strip then in that case it would become people even d m one and at the outlet will become we do d m toe applying the same convention for work transfer to be help Total vote transfers Cueto the blue s that its external work minus b one B one d Yemen plus Pito Pito be this, will you? What if we divide both the sites by Tito? That is the time In terrible. We will get me the Bluebird Ito's kowtow Dita plex by determine its people. We won t d m one upon data plus Pete over a two day and two upon Ditto implies did a blue by D tones called to be double X by ditto minus people even and will not plus B two Ito. And do not why I am not an empty Not because diem on my ditto would be what you were. Um well, not and d m two upon the tow boat. Empty amount. Now this DWS readyto is nothing but extenders right off his transfer. So from the energy question, we can write that I am one not even plus Dick you buy. Ditto school. Tow em to not veto, plus dw by Do you don't just really engine the same? No, as we are seeing in the earlier lectures the specific energy Most what? Especially total. Net us what you want you Plus we square by two plus jet So even an e do that is the specific total energy from in the inlet and outlet would be given by you want. Plus we want square by two plus G gentleman and you took place. We two square by two plus g gentle. So putting the value in the Grecian A. We have what and we're not you want plus even square by two plus Ji Jihad one plus de Cuba Ditto It's called toe I am Do not you do plus we two square by two plus j plus d w bank did no from aggression e what we get after simplifying and when not he won plus of you and square by hopeless G. Jed one plus people even plus Dick you buy. Ditto school Tau and Tau, Not you two plus we to scrap by two plus t j minus p two p two plus d w x 20 since and help is given by Internet Raju plus flu work then putting the value of and help me here Well, I'm well not at you one plus we wanna square by two plus g gentlemen. Plus dick you by Tito. It's going toe toe not as two plus we to school by two plus ci j Duplass. I need a bolo webs. My ditto. So this is your floor in creation. Study for energy was some type of a steady flow engine equation. Us but us. I'm great. This concerns of vehicle it the fluid question Now for study flu we have and one not school . Tow them to not schooled. Oh, I'm not school, Toby. Um bandito as first time until do toys concern so the MBA Tito actual Plus we're square by two plus Ji jihad one plus ridicule upon the top school toe b m upon data as two plus we two square by two plus Geagea took us d w expected We just put the value of and one of them to us be upon veto Now if it divide both sides by d m by Dido What we will have actual plus even square by do plus g genuine plus big you by b m Squalid as true blessed be to square by two plus g jet toe plus b w x by b So this is your study floor Energy immigration are sf doubly In the next lecture, we will look into the applications off acceptably Thank you so much 22. 22.Nozzle and diffusers: no since we know about the study flu energy question. Let's try toe implement with some known devices like nozzle and diffuser. But bread with that, let's understand what is a nozzle and what is a refusal. Another is generally a piper to off varying diameter that is used to direct or modify the flu off, illiquid. Or guess so. Basically, nozzle is generally used for imprison the velocity off a floater guest that is passing through it. And if you can recall from the very beginning from the very first lecture we have discussed about free, expect expansion. That means what transfer doesn't expressing knows, because system boundaries changing. But there is no world transfer next diffuser. And if you size the device for reducing the velocity and increasing the static pressure off a fluid passing through a system, you must have game across the Thomas static pressure in fluid mechanics. You can call it from there now, in order to understand how the fruitful inside off nozzle and diffusion and what kind of configuration are there for different kind of flows, like supersonic subsonic concerning flow. What kind of configuration does not own deficit has that can be known by Mac number So the Magnum but is denoted by M, and it's basically a DYP dimension less quantity that represents the ratio of flow velocity past a boundary to the local speed off son. So basically in mathematical formula feel a miscalled velocity offload by sonic velocity and sonic velocity is jointed by sea and is given by under gamma rt. Now, if the value off, um, is coming up to be greater than one that we regard the floor us a super sonny, if it's less than one, it is called subsonic. And if and if it's a equal toe killing toe the sonic floor or it's an Emmy School one, then the flow off liquid is equal in tow. The sounds phone. But this particular flow that's running flu is very much understand. What? So we don't study it? See, here are some conflagrations. If that's the flu, is sub Sony? Are the Mac numbers less than one? This is the complication for nozzle and diffuser, and if the flu is supersonic or the Mac number is greater than one, this is the floor for diffuser Noser. If you can see here, if you can interpret Then you will see that both the complication a completely different there isn't being the same is the soup in supersonic floor water past the fruit or the gas of water is passing through the configuration gets very much compressible. So we have to counter with the compress ability we have to take into account comes compress ability. That's right, this kind of considerations there. But subsonic flu is the natural flow order in compressible full. So this is the conflagration. So you need to understand this confidential If in exam somewhere is asked only a configurations given anywhere beyond this is, uh what is that? That supersonic flow. This is a subsonic low. This is a sonic boom. And yet hotel isn't the nozzle order diffuser. Now let's a play as of doubly for a nozzle. See, this particular set of is here in Little Rock. It is there and what we're doing, we're covering the actual levels off the nozzle with India medic linings or it's basically in everything more. The debt timelines General Gento are equivalent and people we wouldn't be Toby toe are the initial and final conditions since idiomatic codings there'ii diabetic wall is there so keep transfer would be What do our big Q by d. M would all tropical in tow? Joe. Hey, transfer by unit marches Also, Jill. Also the world transfer budget marches also chill. Why free expansion and kind Take energy. Would not be able to show that you have to keep in mind because we will and we do has a difference. We do would be very much larger than Vivan. Well, a city now that elect and help people begin by attorneys called You want place beyond even and that out late, it can convey Yuto plus B to veto Now now let's a play the study for energy question. Tow this Nigel so it is given by action plus or even square by two plus g Genuine plus D. Q by D. M Squared toe as two plus we two square by two plus G jet too. Let's do the blue upon being and you must keep in mind that you need to see it isn't jewels Park Hee, Right. So this complete equation isn't juice bar cagey? We have to convert it into collegial package e us but us the requirement so initially it is introduced for Katie that you have to bore in your mind. Now, applying all the amount on the contract is here. We have gentleness, Sergio and Hate transfer as well as work transfer. But unit mass is also Gino. So we have what Atlantis were described by to school as toe Plus. We describe it toe at u mass, Pashto that exchanging intel gets could be two square minutes. We want scarred by toe. Now this re one is comparatively very, very, very small. Then we do so we can neglect it. So we have finally traumas has to escort away to scrap by toe. Are we told that is the exit velocity or the outlet velocity that is quibble Underwood toe actual minus esto and destroy in jewels Kitchen again. As I told you earlier that was in juice market. There s f globally now for converting it into a closure. Burke is even toe divide it by 1000. Right? So the question will become What? Actually, because we want square by 2000 plus g genuine upon 1000 plus deep you buy diem is going toe to toe Unless we do square by 2000 plus g Gento among 1000 plus Tita Blue biting. So this because the kilo joule per kiddie version off this time steady flow and education No. With regard to this particular question, we get the exit without philosophy. Years under Hood 2000 at your minds Pashto are 44.72 undertook tell at in Kilo Jewel parking Thank you so much. 23. 23.Turbine & compressor: Now let's have a brief discussion about turbine and compressor and the implementation off acceptably tow them. Turbine is what a machine for producing continues. Power, in which a ville are rotor typically fitted with vents, is made possible by a fast moving flow of water. Stream, gas, air, any food. So basically here the mechanical work is getting done. What did into electrical work in case of trouble and compressor in case off turbine? The work is we're getting work out of the system, but in case of complicity here to do work by yourself. So in case or turbine, the vote done that is the work that is often is forced to encase a compressor. The work done is negative now. Compressor is a mechanical device that increases the pressure off a guest. By reducing its volume, you must have seen compressors in many places where you feel your air in your tires off your car or your buying Korea scooter. Anything. Our cycles. Even so, those other compressors and turbines are very much you will be very much family with thereby if you have a state, any ball plant. So there are lots of turbines in public now Quickly. Let's get into the acceptably portion of both turbine and compressor for the same. Here we have a arrangement. What we're considering is that hit lost is school toe Jill. No hit losses considered here. Reason beyond the same is this is just a typical assumption because bacteria, this is not possible, but two dead. Using our farm land, we have to delete, right? And we're considering that it is a eyes entropic process with the fuel. Maas I'm not and viven en read Water inlet and exit velocity and work transfer for per unit mass. It's not cool to Chito, and V one is equal to it. With this on, things are as you and you're going to school to get to and potential. And you will become chill now by applying. The acceptably were at one place. We want square by two. Plus D jed one plus Dickie body in this car crash took place. We describe. I took place jet toe plus dwp IBM here by putting the values genuine. Did was Jiro and heat lost zero That mistake you buddy in school to Jiro, right? So actually it's called toe Pashto plus DWP idea or by simply in a general way we can write DW Stadium us w right, but it should not be done. But just what simplicity you can do but don't do in your examination, right? The full full one double by the end, right? So at one had begun Scotto as two plus w or W. It's called toe trim manners, too. So this is the walk transfer in case off a turbine. And here what we can debuts that actually that vista and help at the in late. It's good agenda and Talpiot the outlet. Why? Because Paul is to work is often from the turbine or basically from the system now for compressor. Same thing symbolism since here walked on its negative. So here what we'll do I went to school to a two plus did the blue by Diem. Here we have to take the sign Convention out the work and we will get at one school toe has to minus w or w school toe as to minus actual. So this is the work transfer for compressor. So we have understood about the Naza about diffuser about turbine and complacent and we have implemented as F w to them. Now, in the next lecture, we're going toe understand? About three ugly. Thank you so much 24. 24.Throttling Process: welcome. Everyone were covered. A lot of ground as but a study for education or basically, first loft Ahmad enemies for open systems is concerned in this lecture, we're going to understand the throttling process in great detail. Basically, a truck ling process is a process. Enbridge suddenly on instantaneously pressure reduction is seen a large pressure reduction . Seen That candle process is a talking horses. It is basically a thermodynamic process in which the and tell be off the guests or medium remains Constant edge is constant. The name off troubling process can be I so helping process. It's a I cental big process. That means actually school toe edge, toe or, uh, and I'll be in the inlet. Would be couldn't do until being open it. Now let's see some examples so that you can have a broader knowledge for the same. Did this three equipments? This three mechanically cute mints are the best suitable example for a struggling forces. The other partner in crime off a troubling purposes. See, that's even see adjustable oneness there. Then I pull the lever for pending Clower up to 90 degree. What will happen suddenly floatable start flowing and again when I pull it backwards, the world will blows, answered only stop. It would be there. So there's a sudden radios off pressure in the very ferry off the world cap. Let it you we all know about Captain Reaction, certain reduction pressure and pulls plug. They're basically like sponges like If you have seen any wine bottle, red wine or white wine bottle, you can see the confident in the top. They act like that. Now let's understand that throttling process in 3.3 missile points. First point. I have already told that throttling process is a ice and helping process that means and help me remains constant throughout in letting out living help ease equal and all we can see say that you want plus B one viva school to you to press Pito Now for real guess. Let's take example of the same just a wall that were taken, and here we'll take two section section one in section two. So for sectional and help, you would be what you want. Less people even and for Section two and tell people bu two plus big toe to toe. And since a troubling process that isn't helping process that means and help ease constant . It will become equal you want plus B when we want schooling You two plus big toe Are you on , man? Issue to school to be toe three to minus people people, Let's take it as a question one. Holy Christian E Now, if anyone even it's greater than Vito Vito. But if the floor work at section one is greater than the floor at section toe. In that case, what will happen since beyond even is greater than we do. We do. You one minus you do will be negative. As you can see from the Christian right, it implies you pooh would be greater than you won All them prejudiced section who would be greater than temperature section one that cleans this can. From this, we can conclude that temperature is increasing along direction from this is case one not guess toe If the floor work at Section two is greater than the floor get section one. That means we do. It was greater than people. Even in this case, what we will help you want malice you to a sponsored you Only you one is greater than you do on the one is good, and then you do. That means temperature is decreasing a long fluid addiction. So in concise, we can say in throttling process. Certain drop off pressure does not always mean that there will be a deep in temperature because normally, what happens when there's a sudden drop of temperature Asali when they served in proper richer temperature drops? This is the misery cases Masato cases. This happens, but intrauterine process. It's not. All this means that with a certain proper pressure, sudden drop off temperature would be seen. It's not always possible in torturing horses, Mom for ideal gas, and they'll be the function of temperature, right and actually school toe Pashto. That misty one will be equal duty tow the temperature settlement constant for ideal chances we'll discuss about religous is in the second point, and the third point we're discussing more, I guess in this case, M Bridge elements Austin Now one more thing. One very important thing throat killing process is Iten as Intel big protests. That means all throttling processor isn't helping process, but the vice versa. It's not possible that with all eyes in to help, it was just on not troubling punches. Okay, So in the next lecture, we will discuss about a very important equipment in mechanical engineering. That is heat exchange. Thank you so much. 25. 25.Heat Exchanger: Ah, heat exchanger is a system designed to transfer hit between do fools. You control their temperature off one of the groups. Ah, heat exchanger could remove thermal energy from a flute using on air conditioning system or adding thermal energy to a system where processes require a certain temperature to work properly. This might sound complex, but the working off it heat exchanger is very easy. Heart flute goes in and comes out as relatively colder one or ah, gold flute comes in and comes out re literally hotter. So a heat exchanger there's a misconception. Basically, people think that any heat exchanger, the men moto and the sole objective is to cool down and in flute right by passing through some cooling agents. But that's not the thing. It exchange is huge. Just like General Flynn and the magnitude, the direction off hid from that is given by second ultimate enemies. But basically, the heat exchanger exchanges heat. That means gold should be converted into hot and hard should be converted into cold. That is the sole object your figured exchanger. Let's take a peek at the hit extreme that this is a shell and puke type of his heat exchanger, and we're not going into the types off hit exchanger because this is not in the scope of this syllabus of this particular course. But you can see this is a shell and duke type off heat exchanger. That means the use, the small, small dose you can see here. These are the tubes inside off which cold water is past. Our ah hardly could disperse as, but it's the requirement, right? So basically, let's let's take example where we need toe cool down, out float, right so the hard fruit will until from here, and we'll ends it from the side, which is not visible in this big, but it will exit from there when it's and drink from here, it will have some mass florid, and when it is exiting, it is. It will also have a mass flow ridge right, But initially the temperature would be hotter, and finally, the temperature would be relatively called that because off the influence off this tube small small tears because in the part with the part that it will for it, it's not going directly from here today, outside right. It will travel some part with the flute that is hard will travel some part ring, and after that it will reach at the outlet. And by the time being, what will happen? The heat that this comes contained within the flu, that is the heat energy will be somewhat desiccated due to the influence off the colder fruit inside off those most multi use. It ain't now let's understand the energy balance for heat exchanger. Oh, there are some ASM since Foster for that vote. Done is a school to Geo, that is DW by Dein is called Ichiro and Hit Loss on his transfer. His studio, Ardeche You by tm School to Joe and kind. Take energy that Mr Finished entering will asserting the exit. Felicity is equal in segments counting, and this is, you know as well as the datum are same. That potential energy is also you know. Now let's consider this. Let's say the body, the cylindrical body off the road accident that feels just seen is the control volume. All right, so let's let's take the example of a stream. Let's say we are trying to cool down the stream so stream is coming in and steam is going out and toe. Hold on the stream. We're providing cool water. The water is coming in. And what is going out? Let's say I'm not W and H W one at the Mass florid and and tell Be off the water that is coming inside. And I am not w and h W two at the mass fluid and and tell me off water going outside. See, the mass floated is saying right, we're not changing the mass flow rate. No, his team for Stevie Help. I'm not as as the masquerade and as hs one was the until appeared in late and adjust toe as dental in the Oakland No, for conservation of mass What we had I'm in my last amount school, digital and for conservation of energy bl in minus CEO Disparate digital This will you? I am not double vegetable one. Plus, I'm not as a chess one, Miners. I'm not w vegetable two. Plus I'm not s edge. Estos will do geo. So this is the formula. I'm not w w one. Plus I'm not as I just one school toe under W w Do. Plus I'm not as much as two. That means in the inlet the conditions are both. The fruits is a grand do. The combined conditions are both of the outlay. This is the energy balance. And here, let's summarize it. I'm not w What's what? Mass flow rate off water. I'm not s was the mastery it off stream I Just when it didn't help you with stream at inlet and adjuster than help you estimate outplayed actual one is didn't help me afford in the Indian and vegetable with the temple water at the outlet. So this concludes our lecture for new tax Ginger, thank you so much for use, um 26. 26.NUMERICAL on SFEE: Hello and welcome to the goes Let's all a new medical on a steady flow of energy creation. The go shingles Steam is flowing through a nozzle at the mass flow rate off 0.1 G parts again with the heat loss off, five floored. Then they'll be at the inlet and outlet given us 2500 and 2350 kilo. Jewel Burke easy, respectively, assuming Meg Visible Velocity at the Inlet Final, the velocity off steam at Outlet and the twin meter per second. So I spent the question. We're having the inlet and healthy in collusion Per Casey as 2500 and outlet Intel be US 235 Miraculous, super busy. And in the question it is us that the AL collect velocity of this team. That means to be to his else. And it is, it said, yearning the cushion that inlet velocity is visible. So just born in your mind unless and until it is given in the question that the velocity is negligible, don't take it negligible. But it also five kilowatt off hid losses. Also there. So dick you, by D. M. Is given us fight Lord and Mass flow rate is what I'm not is 50.1 kg per second. Now, once we know does study for energy. Question is given by I'm not each one place. If you wanna square by duplicity, Jed one plus you're is a school do and dot as two plus we discover my two plus g j two plus w on my here. I think you in double yet because in the early lecture, I already told you that you can write Dechaume idea. And did the blue idea ask? You enter? But it is not right. It's not right to like the writing down. What? It's a son, mathematically correct. It's not, you know t properly, but for the simplicity you can do. But it would be, uh, beneficial for you if you're so living your discussions for the university exams, right? The food thing that is don't write Q and W right de Cuba and Yemen did a Blue by D. M, respectively. Now this particular creation, this whole equation, it's in jewels, basically, so we have to convert it in Tokyo jewels. So by dividing 1000 we have the new question us. I'm not action. Plus, we went square by 2000 plus GJ one upon 1000 Plus you is going toe m dot as two plus we to scared by 2000 plus gentle by 1000 plus No, we will put on the values here. All right now, one more thing he had w would be digital because this is a noser And in other what happens free expansion So D w by Dee and Arthur Work transfer is you right? And we have what he'd lost heat losses there. So it is really lost from the system. So it would be negative, right? So it will devalue CIA want 1 25 100 plus Jiro plus Geo. Why? Because we want were taken is Geno and that one in that Do they are the death camps. They were also zero right and minus five. That was a five kilo. What school do? 50.12350 Plus we do square by 2000 and we two squared events veto. It is a village to get out. Click here to find after the solving the questions. After putting all the values we get veto that is a velocity of steam and exit us for 47.21 meter per second. Now in the coming election, the next lecture, we will understand about the work and he'd transfer in the open system here. Already established the work and he transferred in case off a closed system in our earlier lectures. Now we're going to stand, please. The open system hit, transferred and work transfer. Thank you so much. 27. 27.Heat and work transfer in open system: Hello, everyone. Let's establish the work and he transfer in case off one system, as you can see here, Open systems what were masked as well as energy can easily going to say and come outside. Onda help! He is young by what I just called to you. Plus Peavey, this all we already know. Let's differentiate the situation off. Enter P. I just got to you press beery, we get BH That's called BU plus D off B B expanding this differentiation d off TV you get Do you plus BBB plus bdp Mom, it's orderly it with a closed system. So this is what didn't tell me for open system. Now for closest on what fear From first law of thermodynamics we had dick you school to do plus de problem and did a blue us What pdv book? In case off your simple system and a closed system that means becue skull to do you plus PDB formerly were simple process. That means we can put it in the question be edges condo bu plus P d v plus V p. That means be edge will become big u plus PDB our big you school Toby a H minus v b b. So this is the hate. Transferring the open system provided that the processes they were symbol So it is valid only for the words will process not for irreversible process. No from study for imaging. Question the very general formula off study for energy questions. What big you? It's called DP that is potentially jeepers DK. The can take energy Plus do you internal energy plus B off PVS plus B. So the basic equation was work. I'm not edge one plus we want squared by duplicity. Jade one plus Q or Dechaume IBM is called Toe. I'm not as to place every two square by two plus Jesu Tomb plus deed of new by GM. But the most generalized formula for study for energy creation is this one changing, potential energy changing kind of energy, internal energy and floor work and extra new book. This DW DP V's were floor work and did a blue is the external work can be electrical can be shopped anything. So open the bracket we have dick you Scotto d p e plus dkt plus d u plus pdv plus bdp plus vida blue. Now from both the sides were having Nick You What be you plus pdv waas dick you for useful process So both the vehicles will be cancel out and finally we have BP plus DK plus deduct . Look at his external. It's going to minus three d being. Let's indicate the public question between any two particle straits with, Let's say, one or two. So we have 12 to minus three db square toe. Want to do BB plus wantedto be game plus integration off DW. Why want to is not hear why there's no lower and upper image because this is a bad function . Depends upon part. It's not a property off the system, so want to do would not be possible because we're not talking with only one state late. This review US changing potential and Cipla's changing kind of energy. Plus, Dexter Networks could do minus off one toe VT be now for study for what we helped change important energy as well as changing kind. Take Energias Geo father of your simple process right Then we have w school minus one toe btp and this is the work transfer in a open system Onley Onley on the applicable to the possible process is not applicable to rest now since for a closed system we have a BB diagram sending will for open system, but slight differences there. In case of PV diagram, you can see the left hand side and the rightness and see you for open systems. Walk transfer is given by the area under the reading room, but the area is getting changed for open systems. The projectionist wants the pressure axis. But for close system projections to us what 20 banks is. Thank you so much. 28. 28.Work transfer via various devices: Now let's have a discussion about the mind compressor and pump us. But its open systems concern us. But us well, can he transfer its concern so black so that we need to help certain assumptions, like kinetic energy should be. Jiro are basically changing. Cutting energy should be gentle, changing potential energy for Bigelow. And the work done is given by minus we integration DP that were already establishing our only lecture. No, from study for energy question we have and my new 20 at it dealing with on three. All together they're buying pumping interest, but the results will differ for different cases. So here we have the study for education and here Q would be Cheeto the gauze for a reversible idiomatic process with Jesus generally implied in case after buying compress and bomb hit transfer is gentle now. Work transfer. It's given by m dot actual minus Pashto. Why? Because we want is Jiro. General is Geno. So what? We left it. I'm not actually plus Q school toe and has two plus w. Now he's also show that means w school to m dot at one minus Pashto and this particular immigration, this particular formula is true for their buying only right. This is true for turbine only. But in gaze off why it is a true for turbine Because we're getting workout off Turbine. As I told you earlier, and I think in many legislative I have focused upon this area that you can see the minds and power plants the bus turbine generate work we don't have to do welcome turbine. It can work. McNichol, energy, toe, electrical energy. Basically, it's a part off a system off a power plant. Right? So this particular question this work done, I'm not actual mus esto. It's true for doubling. Known for the compressor and punk like a dual earlier. We have to do some work on it to get the desired result. So in case of complete sent work done is NATO because we are doing work on the system. So in the case of complacent, bumpy l and all these are for open system, right? W school toe. I'm not as to minus an angel. The workday N'Guesso open system is what minus in tradition really p so we can t quit all this form Last doctor buying complacent from two minus indication GDP that Mr Amputation and says to be equal to minus integration GDP and same thing goes for I'm not as to Marrakech. One for compressor. And so this concludes our lecture. I think you must have got the idea about the water for the buying. Complacent Bob. You know, open. Thank you so much. 29. 29.Work and heat transfer of various processes: No. Let's establish the work. And he transferred in case off different different processes. My castle as a Batic eso coric debating opponent. Arabic. So first is ice. Nobody crosses were precious, constant. Or we can say BP's will do Jiro now for open systems. You know that w school two miles integration with BP. So in case you are somebody process fear about us, Jill. Now, by applying study for energy question, we will get on not actually rescues called to and daughters to press double. Why so because we're considering kind Take energy importation and these cultures of even square by two when gj one would become Jill right? Those two entities will become Joe. Put the sites so we will get what Finally, I'm not want rescues called under next topless tableau. Now the blue is also Jiro. Were Venice also your in case of our somebody process. So what we get que That is the heat transfer. Scotto am dot as to mine, etcetera. So, in case where somebody process book transfer school to Jiro and heat transfer is, um not as to minors. Edge one now for I so calling pluses we have volume is constant. I'm gonna be a constricting finding energy and potential suggestion because and why we're considering all the pain. Because this is a requirement for the study flu. We are assuming that kind intelligent potential is zero in order to make the flu Study not w here is minus integration. Oneto GDP here V is constant warnings. Concepto we will take it outside so they become minus three. Introduction Want to DP or monastery being to minus people? Are we going beyond minus speak? So this is the world Brian gets off, I saw according process and which is valid for And proof or boat I didn't really kiss since , you know, started talking when I didn't guess on. So if you can recall we have identical secretion that is BP's well to MRT so go relating with deprecation. We can also write the work Transferring kids are so quick process as a Marty one minus B and how come pick it right, Because in case if I so could it pushes weaken right for a process between 1 to 2 even could be called to veto and internal Derek will do be that is the volume that is the cost of failure so we can write the book on us. People view and must be treated that way. We can write a month even minus 32 because tidal desecrations what BP's will remedy? No, we're already step. Is the work done and the generate from love? Ogden and he transfer in case of the open system That does what Dick is. Go ds minus really be so By integrating both the sites we get cues will do edge to Manus H one plus p one even minus pito. We too simple integration formulation right. By realizing this equation, we get edge to Manus Pito Pito miners actual minus B one B one. Now, if you can recall the formula for Intel B, what was The edge is cool. Do you bless b? G? You wants what Internet energy NPV was the rule book. So if you take the floor walk to the left hand side we get what internal energy school do and tell p minus for a walk on edge minus PV so correlating With that, we get you man issue One school took you and if some somebody asked debt, what is the heat transfer But unit must on Dick. You buy IBM, then you can write capital. You do minus soon. Because this waas earlier one wants What small. You too, man. A small you one. That was a specific internal energy. All right, No, for India bit medic pulses. We know that the heat transfer is you know, so we don't have to discuss about that. But the work transfer for a possibility Basic process that few discuss along the back was given by what got up on comma minus one people immune ministry to be. And for ideal guess we can relight it. Us W's going to come upon commas. One amount you on my necessity. Now the same thing goes for body profit. Was is also our fault I want to discuss is the topic poses so for a while topic process Also w they hit work transfer is given by an opponent minus one B one B in minutes b two, b 2 40 watts Will processes and Friday process are for I don't guess basically the new school toe and upon and man, it's 1 a.m. r p one minus t. Now buy a plane study for energy. Christian we get and not actual rescue school toe and what is two plus double? So we have been limited political process right now, so there will be a he transfer walk transfer. We already discussed you. Trust would be there. So we're toe find the formula for the same I love you Would be Will do. I'm not as to money such one plus l a born and man it's one people being must be Do it just by putting the value off the vote and in case of a little pink roses simplifying it we get and not CPI into my honesty one plus an opponent minus one people even minus pito b two no , as you know that. See, people see school Tau gamma and see him on a C V school toe are by solving this two questions we get CPI school toe are gamma upon gamma minus. So this is aggression that you can find out by yourself. But this situation is glad for the reduction of the formula. That's why I put it here now you would be you. And by I'm not, are come upon ga minus 20 to minus Steven plus and apart and my son People being Manus Pito we toe that is school to come upon comma minus one b two B two minus people we want plus and upon an minus one people even minus b two b toe. Finally we get the heat transfers could be even V one minus b Do we do upon and minus one Indu gamma minus and upon gamma minus fun. So if you can look closely, you'll find out that this particular dumpy one we wanna speak to we do upon and minus one. It's nothing, Buster. But the walk done in case of Apollo toppy process for a closed system. So finally we can write down the heat transfer Engages with Paul Tropic process for open systems Quito wagon off Apollo dropping process in a closed system into gamma minus and upon gamma minus one. So, in a nutshell, we can see for a somatic process. We help work transfers Jiro and he transfers and not extreme agitation for a so called cooling process. We have work transfers, people minus b two in to be our, um our people ministry to, and he transfers you to malice you one. And for a limited process he transfer Was Jiro invoked for what's gonna happen Garments when Ahmad even ministry to and finally four point copy process. We had w school playing upon in minutes one people being must be to be toe are and upon animal It's 1 a.m. at human Ministry toe and he transfer us the one we want my respect. We do upon an minus one into gamma minus and upon comma minus one or well done in case of a part of the process for a closed system into comma minus and a one comma minus one. Thank you so much. 30. 30.Fundamentals of II law: from the first law of thermodynamics, they were able to establish the magnitude off heat and work prosper. We also had a formula that was Dick useful to D E plus Dita blue and after eradicate important share Maje in kind Take energy. What we had the Q school to B plus d W Where do was the internal energy? No, the first lost time. Would enemies filled at one white it field toe address. The Froome are basically the direction off. Hateful. So here, second off Ramadan, a mix comes into play. The second law of thermodynamics. Use the direction off hateful Now for understanding The second law we have to variants are critical Bruce treatments when it's gallon blanks and 2nd 1 is glasses. Statement. Now, in order to understand the second law, we're going toe again. Take a experimental basically a set up, just like we took juice experiment for understanding or for elaborating. The first law Hamedani rings We're going to understand here through scent of off power. No, the busy companies are poor. Plant is for funniest boiler, turbine, condenser and pump. So in the national, what happens in the boiler is steams getting heated and then being cento thereby. So for that additional, he dis applied for fullness. And inside the boiler these I saw by the darkness, peaceful to see. So the steam that's going out off the boiler has a pressure. Us people. And with this pressure the steam is gliding with the veins or basically defense off the turbine. And the MEC nickel walk done that is generating, said the turbine is converted into electrical. That means we're getting Volk out off the dull by and as soon as we get the work out of the tub. By that miss days, some expansion poses going on because just like I told earlier in in the in that lecture off sign convention for work, that if expansions then we're getting broke out of the system. Or if the compression is there, then we are doing work on the system, like in case of a turbine and compressor. Now, after the turbine, the steam pressure would become Let's Pepito and it will go to the convention and there will be a hit rejection. It was cooling down or something, and after that, if you want to complete the cycle, what we need, we need that the reduced pressure Pito should be complete cooling to the actual bishop, even off the boiler so that the cycle complete. So for that we're to do some at sternal book and that external work is done toe bomb. And so we have great in external work here, and this external work increases the appreciably to people here. P one is greater than people that you must keep in mind and the process goes on it on us. But as the additional, he dis applied to the boyar to the finance Know how many betterment as we're having here? I did it dissected heat walk that we're getting out of the system through the brain and work that we're supplying to the Paul or basically through the pump in orderto elevate the pressure to match with the oil, especially no one really important thing that you must understand that the U does. That date is basically the heat lost deck means all the heat cannot begun wanted into work . There's no such engenders north, a set up that can convert hole, heat and work if such engine, or if such such kind of set up has been invented it will solve all the problem in the world . Now the net heat transfer should be granted the Net voter. That it doesn't means that all the heat is getting converting to work. No, not he transferred through people into network. That is what include princes. So the heat added minus hate rejected people to the work that we're getting out of the system, minus the work that the approach I didn't alert system through the bomb. So the work we're getting out of the system toe turbine in the work that we're providing food system is true. So we can write that you added is called the Blue Net, plus Q Dissected he had double out of certain. That is wrong. We have to right here. W neck. That miscue added, is goingto w net plus Q dissected. Now there's a very important concept. Asparagus, a second lockable Dynex concern that is thermal efficiency. The thermal efficiency is nothing but the ratio of network done to the heat added so it will never be equal to or greater than one. It should be all this lesser than one US butters. The second law of thermodynamics is concerned because if it becomes equal to one that means you. And it is called W Let that it's all The heat that has been provided is converted into a world that is not possible. So this concludes our session, this particular session for second Northam. Adam, is it wasan introductory like lecture. So in the next lecture, we're going to understand about the Calvin Planks this treatment that defines second law. Thank you so much. 31. 31.Kelvin Planks statement: the Taliban blanket statement are the heat engine statement of the second Law of thermodynamics states that it is impossible created device psychotically operating it Injun basically the effect of which is toe absorb energy in the form off heat from a single Permal Zubair and to deliver equal amount off just like you know, only lecture. What you understood that if all the heat that is provided to the system was done, what did in the book, then it will start on the problem in the world, but it is not at all possible. We also established the thermal efficiency. Pita is always less than one that is also given by W. Netapp on the heat. Added Nowadays, one more basically definition off. Calvin Blanc's statement that is, it is impossible for a hating Jim to produce network in a complete cycle if it exchange heat only with bodies at a single temperature. So this in bel possible in case off a heat engine to produce Walter for a complete cycle. If the exchange of feet is with bodies at the single temperature, it is not possible. There has to be different bodies or basically even same bodies with different temperatures , then only at change your feet will produce network. Oh, we can say it is impossible to create a hate engine, which will give no other effect except to extract heat from a single Isoa. And to do equal amount of that same concept. That means it is impossible basically to create the heat engine, which will fetch heat from any source. Let's say a family is aware that were coming toe, huh? Provide equal amount of OECD and, let's say, Tank Low, Jewell off hit Bingle fetched from a hammers aware, and we're getting include Djalo folk that is not at all possible, at least not now. Now let's understand what this thermal energy desseaux varieties no family energy deserve. I am is basically a hate source in finite. His source. That means even if we are, I think, lords of energy. It says that this is a political concept DNA, so you have to understand in data card. So basically, even if you have adding heat again and again to eat, the temperature of the reserve doesn't change it, so that that is what a common energy is aware. So there's a source. There's a heating general days a thing. As you can see in the center, that means the hitting Gen X is extracting heat. Let's secure from the terminology zoo, and that is the source. And after doing of Ogden, it is a decimating the sink. So the network and would be what you want is greater than Kyoto, obviously, so that working with McEwen minus Kyoto now as we know the thermal efficiency, is young by the blue net. Upon que added here, the added heat is what you want, So the blue Net by Q one would be the thermal efficiency our bacon, like you on minus you to upon Q one is called to thermal efficiency, or one might ask you to bite. You show that the question are basically the formula for Tamil efficiency can also be return us. Do you want mine? Ask you do upon you want in case off a head injury. Now again, I am replete repeating the same concept that it is impossible tohave 100% efficiency for thermal efficiency. That means thermal efficiency cannot be cool into one on it cannot be equal 200%. So this guide off set up. That means the amount of heat that has been extracted from the Zubair, and we're getting equal amount of Ogden. So if if such kind of machine is possible, such gonna machine would be called B and AMP. Toe perpetual motion machine, so be an empty is impossible. Thermal efficiency, that is, school 200% is not at all possible. So this couples about the Galvin plans, the statement reached gills rich work producing devices such as Hue danger. In the next lecture, we will talk about close. Here's a statement to define second lot amount dynamics, which deals with what consuming devices like heat or refrigerators. Thank you so much. 32. 32.Clausius statement: No, let's understand about this is a statement of second Law of thermodynamics. As I told you earlier, the process is, statement deals with what consuming devices like refrigerator and hate. It says that it's impossible to construct a device which operates on a cycle and produces no other effect, then the transfer of heat from a lower body to work harder. But that means of external buggies required in order to transfer heat from a cooler body toe harder body. Now, in simple words. If you're having a substance which is at a cool, original vision center must call dust it and you won't do transfer heat from a whole body to our body. Then you have to do some external book. Let's take the example off refrigerator. We all had a frigid to know home and lost most the reason behind it, because it gives the food fresh and how come it withdraws heat continuously from the food and provides it to the single the average later. That means, in order to keep the food fresh, continual good growl off, hideous required. This is one case. Second guess second kind off welcome it consuming device would be hit from one more thing in order to withdraw the heat. What the refrigerator is doing it is providing walk to it. It is gonna did with electricity, right? And it's brought in working order. Auto. Do so in order to keep the food fresh. It is using electricity in terms of work. Amanda Hip. What does he'd from do? Basically, it takes the heat from a cold portion and provides toe harder. And was the implementation of the same? That's if, for example, you're living in a articulation or basically insight. Video Canada Anywhere we're temperature is in Miles Davis outside, but it's still your surviving in this kind of areas. How come do you do with the help of this kind of devices? What hit ponders It takes the heat from the gold portion and provided to the heart abortion ? That is your room. And that's why people survive in this kind off severe environment. Now, let's understand both. Refrigerate any heat pump in grief. See, this is refrigerator here. Stephen is the sink, and Tito is the source. Same things for him. This one is doing is testing and to do the source. Both are looking same, but only one is different that our referees return in this one, and HP is returning this one. So this is a demotion for refrigerator, and a heat pump set up is exactly the same. But the desired effect or basically the implementation is completely different. Just like just just I told you earlier that definite traitor continuously withdraw heat from the source in order to keep the food fresh, are in order to keep the substance in one particular template. But what's the men won't go behind. Hip amusing hit promise to withdraw the heat from the cold regional court substance and provided to the heart of our right. So there is one Newtown that is called coefficient of performance. It is given by the design effect by work in now, in case off refrigerator. That desired effect is what the design effect is to keep the food fresh, and in order to keep the food fresh, you need to keep it in one particular temperature, so the desired effect would be cute to in this case, and in case off a hate bomb, the desired effect would be worth your to supply heat right. You you have to gather heat from the quarterly production and supply into the hot arisen. But that means I respectfully or terrorism. So here Q one would be the design effect. So the formula for efficient of performance for a fridge Ritalin hipbone will beat you to buy Dublin Que on bendable respectively. So, dummies here. What do you want to ask you to? Both the cases. So we have you do a bunk, You on mine ask you, does the coefficient of performance or C o b o for the fridge traitor and Q one a punk, you unmask you do it. The coefficient of performance for heat pump Seop off. Now, this one conclusion can be June here that this seop off, he probably school to see appeal for a fugitive plus one, you can define it other ways. You can die the same range. So we have done with the Galvin plans as well as the losses this treatment off Second law of thermodynamics in the nest lecture. We will talk about garnered cycle and cannot thank you so much 33. 33.Carnot cycle: a guard, not cycle, is an ideal, not my words. Ideal reversible closed thermodynamic cycle. Invade. The working substance goes through the full success you oppression off. I saw thermal expansion toe desire Point, a diabetic expansion toe, a desired point. I saw time, a compression and a devotee compression back to its initial state. So it's so complete cycle are it's basically every worst civil Sagan now, in order to understand what cannot cycle is, let's stick a BB dining room and here we have 12344 states. Four points are there and here. Four basic for assistance is happening from one to do I so terrible expansion is there. I saw Tom Elements. Temperatures construct right. And then Toto three is what a diabetic ex mentioned. That Miss he transferred studio there again through before Is I suitable compression and then 4 to 1 is a good idea, but accomplish so this is the whole set up off. They cannot sacre And what's the need off guard not able on the business off? Cannot Sager. We get an ideal situation which can be used for many of France's. That's why we study cannot say no here, as you can see, since I saw thermal expansion is here, hit Addition can be done from 2 to 3. A dramatic expansion is there. So us, I told earlier. If a system is undergoing expansion that we are going to get work out off it, that's why work we're getting the workout off it. And then compression is that I saw Tom A compression says I suitable compressions. Their heat would be dissected. So he is getting out here. And then again, anybody compression. Since it's a compression for compressing, just like in case a compressor, we have to provide vote from the outside. That's why we are having walking. Put here now Let's make the PS TEGA temperature versus entropy are in trouble with his temperature. Also, you want to call here. Want to do was one. I saw thermal expansion, so temperatures will be constant and heat addition is also there. Let's sit. You want toe from Doubletree. Idiomatic. Just mentioned is there so it would be again a Strickling and we're getting work out off the system. Then beautiful were again having I saw thermal compression. So he does win. Resented you 34 again 4 to 1. There is a remedy. Compression. That means they have do, compressed the system, compress the cycle, and we have to try to work from the outside so it would be gone by W four. What another corresponding release would be the only be school to Tito NT three school boot before, as purse, temporal distance and and for in property well as when it's will do as four and as preschool toe as three. Now, from first locked Ahmad, enemies from the Jews experiment itself. We know that Q. Net is going to Dublin it, and here you never will be Q one to minus Q 34 that Driscoll took you to three men ask you for one. Are you want do school? Do as two minutes as when Stephen and Cute three Force will do as two minutes as one. Petri. Why so because just like BB diagram, the area of the baby diagrammed uses what walk? Transfer. Similarly, the area under the PS diagram use us what he transferred. That's where you look you want was caught west to minus s one table and cute 3/4. Good estimate says from Peter Simple German tree. Now the neck work done is what you want to minus you 34 for canon engine we have What turmoil if urgency as network upon net here dress for now here, network is what Cuban too minuscule. 34 That is the one as two minutes as one man. It's Petri as to money, says one upon the one. As to my assessment, that is, that you added WNET upon que added right, that is, even by the one minus 21 R one minus t three by one. So the thermal efficiency would be what one man's 33 bite anyone on we can see thermal efficiencies were toe one miners and Bridger up the sink upon temperature of the source. But it no listen. This trend the Khan Attila the Cano Till stairs that no head engine working in a cycle between two constant temperature reserve wires can be more efficient. Dinner reversible engine working between the same result. That means the efficiency off a heat engine working, working this cycle between two constant temperatures of oils and if in the same constant temperature, is the wires are reversible. Eating dinosaurs were working that it is not at all possible for the prior heating. Jen toe have efficiency more than that off Very was bleeding. That means, in other words, it is that all the engines operating between a given costing temperatures source and given constant M buttressing none has a higher efficiency dinner. They were Sillinger. I bet it must have sounded very much confusing. So just look at this particular graphic and you will understand. See this too, are the source and sink and bought. The reserve wires are maintained at a constant temperature. Now that at E that is returning The simple contingent that is working between this true constant reserves and H e r is that reversible heat engine. So the counted two rooms is that this actually are this reversible huge engine will be undoubtably all this more efficient than the edge. Even so, this is all this more efficient that this one Thank you so much 34. 34.Reverse carnot cycle: now let's discuss about he was cannot cycle. See in gives away cannot cycle that we're discussing the only a lecture. It was a totally reversible cycle, which consist straight off to reversible I September processes and to ice and product processes in case of Donald Circle. What beard I saw thermally tradition, followed by ice entropic expansion followed by so Turman, heat rejection and finally as entropic compression so we can conclude that cannot cycle was a clockwise oriented one. But in case all of us cannot cycle as the name suggests, all the processes are just reversed on. Oppose it off cannot sick. Here I sent tropic compressions there, followed by I saw thermal heat rejection followed by as and prophet expansion. And finally it's a German, he Danish. So we can conclude in case off us cannot cycle that it is a and piccolo price oriented kind of second. But one thing is common in both the cycles that the integral off closing jiggle off doctor and hit transfer is equal. No, the carnal cycle waas useful work, creating awful producing devices like he didn't you, but that he was kind of cycle backs up hit bump and refrigerator in which we have to parade book in order to get the desired result. Now the coefficient of performance in case off formula feed registered that we have already discussed what we had desired effect by walk, input or work net that we're getting. So in this particular center we can write coefficient off performance or Copco will do you do upon W network. You took one Cuban man executed because Kyoto is the design effect. Why so? Because, let's say, for example, we need to keep food fresh so there to continuously gradually extrude hit out off it in orderto ledge. Imminent fresh. That's why que toe is the desired effect. And Dublin, it is obviously Q and minus Kyoto now engaged or hate bomb that desired effect, just like I told you earlier in the lecture. The example off. The Arctic reason you're living in Arctic reason and you want to go make your home bit warm a bit former or would basically Roma, then the bazaar atmosphere outside, then the cool atmosphere outside part of me words. So in that case, the desired effect for big your so the coefficient of performance off hate bomb is what you want by double net Acuna by you and mine ask you to. And that would be willing to be one upon people minus Tito in case off reversible condition . Right, No malice. Take example off for refrigerator for reversible case. We have you to appoint your mask. You to school to Tito Puente, UMAss, Tito. And if it is reversible Cute. Open your mask. You too would be less than Tito won't be on my ass, Tito, Because off what I cannot tell him it was what gonna till um, suggested dead. I mean huge in jail that is walking between sim sources off reserve errors or Tamada's arrests the same thing and saw us off reversible heat. In general, it will always have the efficiency. Lesser than that he was in danger. Now these are very important for Miller, whose dedication I'm not going to do here. I might give it assignment. That efficiency already was affiliating. Jim school do one upon coefficient, off performance off a heat pump. This is a very important formula that your true remember? Thank you so much 35. 35.NUMERICAL on II law: hello and welcome to the course. Since we are going to complete this particular section, let's do it in style and that's all of your medical. So basically, we're going to solve do Michels here. The 1st 1 goes, Ah, bless since is that he has developed engine that Digs 105 Make a Jew in at a temperature off 400 Calvi and Gazette's Four People Mega Zoo at the temperature off 200 killing. By doing so, he says that he delivers the work off 15 kilo. Can you tell if the person is telling the truth or not? So, basically, to solve this particular numerical, we have to make the arrangement. So as far as the Americans concern, the person is saying that he has developed this particular hating in which, from 400 Kelvin, it is aware Tom Eliza Weir. He's drawing how much 105 mega June, and he's dealing somewhat. 42 mega zoom to Don't think that is 200. Tell me No in this whole process, he's a I think that his didn't work off 15 kilowatt hour. Now we have to establish if this particular person saying true things off all his telling truth or not long, let's compare this, particular persons said, injured with irritable hating. So for the same, we're having this particular arrangement. And as for this cannot tearing is concerned. The efficiency offer reversible Heat engine would be always greater than this person's it injured. And if this particular state wave, this particular pyramid's getting relegated, we can assume that the person is not telling right. So let's find out first the thermal efficiency for a possible heating and that is also operating between this to preserve us. That is 400 Calvin and wondered. So for that, what formula we had one minus two to buy Dune. That means one minus temperature of the sink to the temperature off source that miss one minus 200 by 400. That means the thermal efficiency for a reversible heating gel. Walking between 400 Calvin and 200 Calvin is 50%. Now let's find out waas the thermal efficiency of this particular persons heat engine. Here we will use the net Walton and the added heat. That means the blue net upon que, uh and what we can write Issue one minus you Toa Que because the net for dinner for this particular heating Jim off the person is U minus cuter. What we can. I wanna ask you to make you who solving what we get. The thermal efficiency off this said hit engine is coming up to be 60% which is 10% more than the thermal efficiency for a reversible heating connecting between these two sources. So which is not possible that the person is telling a lie. Now let's proceed to the next question. The cushion goes, Ah, hit bomb Working on cannot cycle bigs he'd from is aware at five minutes senses and delivers, he told. Deserve I at 60 degree senses. The hit bomb is driven by yet your civil huge engine, which takes heat from others. A wire at 840 degree Celsius and rejects him to reserve are at 60 degrees Celsius. The reversible you'd engine also drives a device which absorbs 30 kilo. If the heat pump expects 17 kilo Jewell parts again from five degree senses with the wire debt remain the rape off its supply from the Internet 40 degree Celsius source and the hatreds acted through 60 degrees Celsius. Think now here. In this particular caution, there are three players. One is a hate bomb. Another is a hate injured and one more device, which is absorbing Tadic lowered from US Bulletin gin, right, So by looking into the ocean, it looks very much complex. But if you'll make arrangement first, if it tried to see what's happening, actually, then you'll be able to solid in just a blink off. I. Now let's make the arrangement. We have a heat from a huge engine and a device that is in between them and that is delivering a book off. No for heating Jim. The Heating Journeys. Taking heat from Reserva that is, at 8 40 minutes senses and presenting the heat to the result where, at 16 instances, the hip hop, on the other hand, is taking head from five senses of the wire, and it's presenting at 60 degree senses. Who's over? And this didn't business. A particular arrangement justifies heating generated from itself, reigned no. As you can see, 16 degrees Celsius is common in both for the heat pump as well is that he injured so we can make it a common is aware and we can change the elections, as you can see here. So let's write down. What what are the? And I did this you into us. We have here Q three school to 70. Nick Lord Evil is going do Triple 13 Helping Did Cruz will do 333 calving? Why so because we're just changing, decrease assessing toe Calvin by adding with 273. All right, don't get confused. T three is five less percent effectiveness by princes. It was presumably three schooled to 78. Kill me and P for escort duty to school. Do that is what the common is aware that we have taken. 16 resources have been 60 plus bonus entity that kids 333 now. The coefficient of performance for the heat bump would devote desired effect upon networker . That means Q four upon Q four minus country and for a reversible heat engine coefficient. Performances would be for one before minus B three. Right, And one more thing. Just look losing in the cushion. The heat pump is ruined by a reversible hitting. That that's why we are taking the coefficient of performance are very watchable. Hitting Jim we're not taking just the heat engine because in case of possible heating gender, call future performances in terms of temperature itself. So it is to you for 20 for minus tea tree. So that is after putting the values coming up with 6.5 long, this U three plus de Malibu would be Q four, starting with scene and putting the values in the official off performance for the heat bomb we have what you three plus doublet Opondo, glutinous contents explained. 05 showing the same we get. Finally, the the side walked on. WTO's Cueto three point 374 Kill What? No. W one is quite little w do blessed, tacky. So what? Waas a w two that we just found out. 3.374 That means W one is called the three countries and four plus 30 that is water work produced by the Hate Pump 33.374 killed. Now what is asking the question? The weight of its A plane from 18 40 divisions and source and second, that heat exacted 16 senses, right? So first, since the heating is reversible, the thermal efficiency would be what? One mystery to back the one we just establishing the serious lecture also, and in this particular question, also have told. So that would be one minus 3 33 point triple country that uses points out on soon it is given by double net upon you add it. Are you one basically? So from here we can find out Cuban that is 47.6, and this is the tradeoff he'd supply from 18 40 divisions issues right? Seven. The thermal efficiency would begin by one man. Ask you to break your that means 10.7 school, the one mess Q two and Q one we found all right, not 47.6 So and this gives us cute was 14.3. No, the coefficient of performance for them. What you're hit Pompeo's you for upon the blue toe. So here, careful would be called Do Cough syrup often is into the little and coefficient performance we have found out earlier that was explained. 05 Soak you for maybe six months. Year five. Minto 3.3 Selling for so solving it. We get cue for us 20 mindful therefore, the total he transacted to 60. The resource will be what you to ask you for? Because extra degree Celsius wasa common is aware. So totally transact would be from the heating jazz villas They hate Tom. That means we help you to rescue for and both the values we're hearing. 14.3 and 20.4. So the final answer for the second question is 34.7. What? So this candles our section off second love Monix The next section would also be the last section. That is an problem. Thank you so much. 36. 36.The order of randomness: hello and welcome to the course. We are closing into the end of the course, and I must tell you one thing, that certain portion thermodynamics like useful work, off label energy and drop regeneration yourself stands all this kind off. Our topics comes under and once thermodynamics. So I would try my level best to bring it to you as a new course on. I would like to add it in this one only. So stay tuned for that. And let's begin with the last section that is Andrabi and Robbie's. What and probably is the Missouri off randomness are this. Order off any system. So basically via tryingto one, define what Gillis sees and rob Izzo's chaos. Basically, thank you knew us what we understand about the universe. It's expanding. So what we can say that drop e off. You know what is always increasing? This is what the more human beings understand. This is what our instruments are. Telescopes tell us. So there's go Bob and dropping is very lost, this small world and probably has a very, very big meaning on the Bt's Off this, we can even predict the big mentally, so that's a very broad expected, but we need to learn us. PARIS The system off thermodynamics is concern. No Inter Madonna makes, then drop e. Hence the amount off permit energy, which is another label for useful work. These are very important to remember and properties concern that is called closest to him. We are already that I Understatement That was close is a statement for second law Thermodynamics. Now the closest serum comes into existence that basically business and Poppy. No, but I acted that we need to understand a very important concept that is reversible area. Batic lines cannot intersect each other, or basically through ice and profit lines cannot intersect each other. Now let's prove this one why we're doing so Because we have to understand closest to room. And for Closius term, there is some dramatically interpretation. And to understand that you must understand this concept. It's less beginning in order to prove that then two reversible idiomatic lines cannot intersect each other. Let's intersect them first in a baby tiger, as you can see here, this a B and easy under the Mosul area, pick lines that were intersecting and point in, and these two lines are joined by lt was symbolized. Term process. Why very using Re hospitalized with German process? Because we want hate addition because we want to convert it into a cycle so that we can prove that they cannot intersect each other. Now says this is a surprise for tomorrow Process rewriting hit here and this is a complete cycle. ABC a right. No, the area under the baby diagram is what you look right. That video established a long time ago. So here, as we can see, the area of this particular triangle that is, ABC would be what the Net walked and the network done would be equal to the night hate principle. It has to be should be because, as POTUS first love, thermodynamics is concern us. But it's the jewels experiment that we're studying in detail is concerned all the work that this transport should be quinto them your transfer. But the wise was also impossible. So we're coming to that. So basically in the cycle ABC that he'd added is from a single is aware at constant temperature t that that were also assuming that the heat that is added through B C, which is a possible settlement process is from a single is aware. No, this cute eight. The Baltic, you add, it is the single is a very in Dublin. It is the natural I was. You have studied the Kalman Blanc's statement. This is a clear violation off second law because perpetual motion machine off second kind is not at all possible were sold a numerical on the basis of same as well as we have studied in the second off Hamed enemies that as part of sculpting plants treatments concern if a few danger is deriving hate for months single reserve wire and delivering same amount off book. Is it possible it is not possible? That means without hit rejection it is not possible. So So this goes without saying that to reversible a diabetic lines cannot intersect each other. Our began also modified the serve particular straight men. And we can say that any reversible thermodynamic path can be replaced by your jack part consisting of two reversible. It abetting and wonder what symbolized the process such that the heat transferring the old process will be equal to the heat transfer in the eyes of thermal processes. So this completes our introductory session off this particular section off and copy. Next lecture will be the last lecture in which we will understand that Blasio's Tura in the coming future I would add a new nickel for this and proper section. But for now we are going to end in the next like yourself. Thank you so much. 37. 37.Clausius theorem: in the last lecture were Stabler's bet. Any reversible Param autonomic part can be replaced by a jet park consisting off to reversible, a diabetic and one reversible I sorta money process. This replacement would be first, that the hit transfer in the original possesses will be corporately transponder. So terrible process. Now, let's imply this particular this Cody From what? Various lecture? Let's understand the closest to him on the business off it. As you can see here, it's a baby tiger in which a particular processes given a reversible process, but in a very erratic fashion, because this is what actual process looks like. No, the black lines that you're seeing are reversible idiomatic processes. So these lines represents a reportable civil idiomatic process and the red girl lines other Your symbol. I saw Temple Process, which are joining to con security areal civil idiomatic process right now as but it's the definition. The discovery that we have met the hit that is added to the possible short term process is equal to the hit transfer, off bag object part. That means the part that you can see here, let's zoom in and see the part that you can see here, this one, this one and this one that would be equal to one process. And the same goes for the dollar bottom essential Here, here and here, Right? No, If you pay close attention here, you will identify that. This particular this whole a system, this whole process this whole cycle Inside this elemental street, it's not nothing but the car, not sick. That means to reversible. Everybody processes as well a story with supplies, autumn processes and the constituent heat. And each and then the heat predict rejection. So for this particular element else triple that said this one the thermal efficiency would begin by what one minus the he presented by the heat. Added, that is your sector calculated. And that will be cool toe one minus temperature at rejection and the temperature that is going to one minus t to buy even are. We can write one minus dick. You wait, Do you do my dick? You one is called one minus two to bite. Even as barista element abortion is coming consent. Right now this implies that did you to buy D D. Q one is called duty to buy demon. Are we can I get you to buy Tito Square toe? Eat you one bite even. No. If you see closely the hit Riz action is taken place here. Let's see it again. Your protection taking busier for this particular element is strip. And that is a weird denoting it with Dick. You too. So as was the sign convention off transfers concern he'd riz acted from systems taken us. What can I get you? So let's put the same convention here. So it will be my last dick You to bite It was called Oh, Did you want make demon All we can write, Dick, you won backing one plus did you to bite? It was equal to zero. And this is for the first Elementary cannot cycle for this particular element of strip. Right? So similarly, there will be a number saw for elementary students. That means due to three by DT plus deep for by defense called Kojiro. And did you four by before plastic You fight by the five school Tojo and so on. So on. So on a to pick you and minus one by P m minus one plus big you and bite again. It's called Jiro. So if we add all of it, what we get, dick you want, maybe even plastic you do by Tito Plastic three by three upto when Dickel and maintains called Jill. So this gives sigh clicking struggle for reversible process Big Q by D Squared Do Gino, this is your Brosius to and this conclusive theoretical abortion off the and Bobby Thank you so much for your time, your patience and hard work. And in the coming future, I might add certain moon tutorial, certain more lectures regarding and probably section anyone more. Thank you so much. It's been a pleasure.