 Okay, so you want to do one more graph conversion. Okay, you see this. Suppose this is VT graph we have, converting to TV and then PT. Try this. A to B, B to C and C to A. Done? Okay, okay, I'll see this. Assume this line is passing through origin, right? This assumption we have. Okay, understood. So B to C and A to B. A to B, the process is what? Quickly, I'll write down this. A to B, the process is isothermal. If you have any doubt, you can tell me. B to C, we have constant pressure process, isobaric. And C to A, we have constant volume, isochoric process we have. Okay? First of all, we'll see isothermal. So isothermal, I am taking like this. Graph we have, so AB will go like this. Which one is A? Which one is B? We'll see. AB will be like this. AB is this AC, CA is constant volume, right? So we'll have C over here, go like this. C, A, B, is this correct? CA will have constant volume. AB will have volume decreases. Actually, AB volume decreases, no? See, AB will have volume decreases. Here the volume is increasing. A to B, once again. C to A will have constant volume. Constant pressure we have B to C. B to C, if it is up, then A should be down. Achha, if it's, take this as C. This is A, this is B. A to B will go like this. Then we'll have B to C like this. Constant pressure C to A like this. This is the graph we have. It's correct? C to A, you see constant volume. A to B will have constant temperature. B to C will have constant pressure. This is the graph we have. B to T, P and T. AB is isothermal, so we must have one line like this. Okay. A to B, we have volume decreases. Means pressure should increase, right? So I think I would take AB like this. Okay. Then volume is constant. So volume is constant we'll have for C to A. C to A, the volume is constant, correct? So C to A, the volume is constant. So if I just roughly, I'm drawing one second. C to A, if it goes like this, then C to B will have constant pressure. Okay. So the graph will go like this. I'll shift this graph on the left side. So we'll have this line. This is the graph we have. So we'll have A to B, A to B volume decreases. Constant temperature. Constant temperature, volume decreases, pressure should increase, correct? So we'll have this one. A to B, and this is C. AB, BC, C. Look at this graph. Is this correct? Tell me. All the process, everything you can understand here, it is coming out to be right. Yeah. So this is the graph we have, right? Fine. So this is the answer we'll have, right? You check your other things, Suresh, okay? This should be the graph we have. Okay. So you have to, you know, you have to, again, think about, you know, one process you just take, place it here in the axis, and then you see whether you have the other points, whether we should have the other points on the left, on the right, have a guess on it. You will have the final graph you will get after some time. You will have better understanding of it once you do some more practice, you will understand this. Anyways, so next we are going to start very two important process here, that is reversible and irreversible process, okay? Heading right down all of you. First, we are going to discuss reversible process. What is reversible process? You first try to understand, okay? I'll just give you the important points here, but first let's understand this. To understand this, we are taking a piston-cylinder system, okay? Copy down the graph, this figure with me, all of you. So I'm taking a piston-cylinder system here. This is the piston and the cylinder we have here. Same piston-cylinder system we have here. Same thing, there's two different states we have, that is it. So what happens here, you see, we have some gaseous molecules present here in this cylinder, and here the piston is static, right? This is static. Here we have gaseous molecules present. It's the same system at two different states, that is it. So what happens here initially, we have the external pressure, P external, and we have the internal pressure, that is the pressure of gas. Now what we do, it is here in the equilibrium, right? Now if you place a stone on the top of it, what happens then, could you tell me? If you place a stone, you will disturb the equilibrium of this pressure and this presence, yes or no? The piston will come down a bit, correct? Yes, piston will come down, okay? So you are increasing the external pressure, try to understand it this way. You are increasing the external pressure from two delta P, means P plus delta P we have. Slightly the pressure increases, the piston will come down, even if you are not observing it, it is not visible, because there is slight increase in pressure. So the piston will come down a bit, you won't even observe it, that the piston is coming down or has come down, but it is there, correct? Again, you do this once, external pressure increases, there will be a bit of compression, and then again the equilibrium went in, correct? Yes, all of you, tell me, yes, correct? So this is one step, first step, next. So this is state A we have for example, state A we have for example, and this is state B, two different state, like I said, we are going to understand. We want to go from A to B, that's what we are discussing. We want to go from A to B, we increase the pressure, what is this I didn't get you, Anurag? What is Dp by Dg is equals to zero, what is G there, what is P external? No, no, why this expression for I'm not getting you? I said, I said, we increase the external pressure, compression takes place, piston will come down, and then the equilibrium will be maintained again, the piston is balanced. Any doubt in this? Correct, okay. We want to go from A to B, again we'll put one more stone, again it'll come down, equilibrium maintained, step number two, step number three, step number four, and suppose this, you have increased the pressure to a certain extent, and then we have reached this state B. So this compression is done slowly, isn't it? One by one, one after the other, one step, then second step, third step, fourth step, like this it is going, means slowly you are increasing the pressure, right? So this process, when you are increasing the pressure slowly, we are taking an example of compression, same thing is possible with expansion also, just you go back, you remove this stone, this stone will come up, again come up, come up, come up, and you will state, you will have the state A again. So this process, whether it is compression or expansion, this way we call it as reversible process, correct? So reversible process is extremely slow process, one by one it happens. There are infinite number of steps. Here we have talked about four different steps just to make you understand, but such infinite number of steps possible because we are increasing the pressure by delta value, P plus delta B. So increase is very small, almost negligible, you won't even feel that the piston is going down, but yes, slowly it is going down, right? So this process is reversible process, any doubt in this? Yes, tell me, any doubt in this? No, tell me, external pressure is constant or variable here in this process? External pressure is constant or variable? None of you there? No, it is not constant either, you see. You have done this in physics also? Reversible, irreversible? Have you done this thing in physics? See what happens, we are increasing the pressure slowly, no, then only the compression is taking place. So one by one you are putting in this pressure, the stone you are putting in and pressure you are increasing gradually, right? And hence it is coming down. And hence what we can say, the external pressure is not constant, very important one it is. The external is not constant, it is continuously changing. Understood? Right, and now I can see problem, it was not there. Anyways, so this is not constant, very important information which we'll use in derivation also, right? We'll see that derivation, how do we do and how do we use this information? But this process, reversible process, you can have many properties of it that you should know. We have taken the example of compression here, same thing we can happen other way also that will be the case of expansion. Suppose you have state B, right? You remove this stone one by one, you will reach out to this point that is state A, that will be the case of expansion, okay? So reversible process can be compression, can be expansion, anything. If external pressure is increasing, it is a case of compression, external pressure is decreasing, it is a case of expansion, both ways possible. Some properties of this you write down, very important properties, write down, I'm sorry. Write down, it is bi-directional, it is bi-directional, means both way it can move, right? You remove the stone, you'll get this, right? It is bi-directional, this process can be reversed, process can be reversed along the same path, along the same path, third one. No external work is required, work is required to restore the system, system to its original position. Just you need to remove this, nothing much you need to do. Third property, write down, third property, write down. There are infinite number of steps and each steps are in equilibrium. Number of steps, each step is in equilibrium. It is an imaginary process, ideal process, like we have ideal gas. This process is also imaginary process, is not practically possible. Extremely slow, extremely slow process we have. Each step is very slow, most important property, P external is not constant, gradually we are increasing the external pressure. If you decrease the external pressure, that would be the case of expansion. And we can apply PV is equals to NRT at each step. These are the properties of reversible process we have. See, we are increasing delta P external pressure by a very small value. Suppose the value is P external is given, suppose 10 atmospheric P external. Now you have increased, you have decreased the external pressure to 9.99 atmospheric. You have decreased it. So that change in pressure is very small. So the process that the piston that comes down, or you have increased it, for example, I'm taking, 10.0001 atmospheric. So the piston that comes down, that shift is very small, because the pressure that you have increased is very small, large increase is not there. So it will slowly goes down. The piston will go down slowly. And that process, the movement of the piston that we have, it is extremely small because the difference in pressure is not that high. Pressure difference is what? 0.001. So pressure difference is not that high. Process is extremely slow. It will go down, attains equilibrium. Further you increase pressure, again go down, attains equilibrium. Like this, it happens in a stepwise manner, correct? And each step is in equilibrium plus extremely slow step. Any doubt in this? Anyone in doubt? No. With this graph, you will understand it in a better way. You see this graph, first of all, I'll show you. It is the reversible process graph. We have pressure volume diagram, for example this. So when external pressure increases, we'll have compression or, you know, quasi-static is a bit different from this. Quasi-static is a kind of, you know, a reversible process only very slow, but there we'll have friction also. Means every time it is not a quasi-static process. It's a similar one, but not exactly same. Now you see what happens. If external pressure decreases, expansion or compression? If external pressure decreases, expansion or compression? Expansion, correct? Suppose this is a state A we have. We have some external pressure here. Now we decrease the external pressure. So we decrease the external pressure to some value, intermediate value, but once you decrease it, in this course we'll have some expansion like this, you see. This is the expansion we have in this, expansion. Further you decrease the pressure, we'll have again expansion here, like this expansion. Further you decrease the pressure, we'll have expansion again like this. And like this it goes, right? You keep on decreasing the pressure, we'll have expansion like this. Are you getting it? This is suppose we have a state B at this point. This is state B, A to B. So all these steps we are counting, this is infinite number of steps we have. Like this we have infinite number of steps. I have drawn this just to make you understand, but like this we have infinite number of steps possible, extremely slow process, and the entire process if you see, it goes like this from this pressure to this pressure. Like this it goes, correct? So pressure you see continuously changing from here to here, we'll have this expansion. Then again the pressure decreases, we'll have this expansion. Again pressure decreases, we'll have this expansion. Pressure decreases, we'll have this expansion. Clear any doubt in this? No, right? On this process, because we'll have the application of it, if you don't understand how to derive work done in isothermal reversible process, you won't understand it, right? Isothermal, you must have done work done in physics, no. Reversible isothermal expansion process, work done. What is the formula we have? W is equals to, could you tell me? Minus 2.303 NRT log V2 by V1, remember that? You must have done in physics, yes? So this work done, I'm just deviating from this topic a bit so that this is just to make you understand, you must have calculated the work done, the formula is 2.303 NRT log V2 by V1 in physics, correct? How do we derive it? Do you remember that? How do we derive it? How do we derive it? W is equals to yes, minus p external dv, isn't it? And then what we do? This we integrated dw, we integrated zero to w and we want, don't write this, okay, we want to V2. Now the question is, why don't you take this p external out of the integral sign? Could you answer this to me? Why don't you take this out? Why don't you take this p external out and devi just you integrate, why? Because p external is not constant for reversible process, remember that, right? So this you need to know. If the process is reversible, p external is not constant. And hence, we cannot take this out of the integral sign. You have to substitute it here, NRT by V and then you have to integrate it, correct? Right, that's why it is important to understand what is reversible, irreversible process. If it is irreversible process, we'll discuss irreversible now, then we can take this p external out because irreversible process p external is constant over there. And then directly the answer would be minus p external delta V. This is the work done we have in all irreversible process. Did you get it now? Yeah? Have you done reversible, irreversible process in physics? Okay, no problem. So this is the reason we have, why p external we took out of the integral sign? I can directly tell you, p external is a function of volume here. That's why we are not taking them out. But then we'll do this mother later on. Let's not focus on this formula. I'm trying to make you understand the importance of these two process because when it is irreversible, we have taken this out. But in reversible, we don't take this out. So reason is this, the one that I have explained, right? That is the first thing you need to understand. No, p external is not constant. That's what we are talking about. I think we're talking about expansion or compression. That is only possible when you change p external by some value. Yeah, if p external, we cannot say it is not constant. If the equilibrium is not reached, I'm discussing this irreversible, that's the second mother. See, if p external is not constant, then the piston would not be at equilibrium. It's not like that. Obviously, see, it's the hypothetical question Aditya. We must have some external pressure, right? So that pressure is constant only if you're not changing it. We are changing it out. It's not like it's happening on its own. We are putting the stone there. We are disturbing the equilibrium. We are increasing the external pressure. It is not happening on its own, correct? So it's not like p external is not constant than what happens. p external is always constant. External pressure is always constant. We are disturbing it, understood Aditya? Yeah, so this is one thing. So I hope you understood now the reversible process and why p external is not constant in irreversible, in reversible process. Now I'm going back to just make you understand the second process that is irreversible. In reversible, what happens, you see here? See, what happens here? Suppose this is one kg block we have a stone. I have put in, means total you see, I have put in four kg of block slowly. And slowly this piston will go down and down and reaches out to state B. Yes or no, I want you to respond here regularly because it is very important. Then only I will be understanding that you are getting it or not. See, so one one kg, just for reference I'm telling you, one one kg we have taken and slowly I put it here and then the piston will go down and will reach this state B. What happens, this is one way we can achieve this state. Why can't we put a four kg block here directly? Can we do that? Instead of one, one, one, one, one, I'll put total four kg of brick over there and piston will go down suddenly, right? Piston will go down suddenly and attains this equilibrium state. Can we do that? Assuming that it won't collapse, yeah. Yeah, piston is massless, correct. Piston mass we're not considering. Assume that this whole system will not collapse. Okay, it is wrong enough to sustain the weight of that brick. Okay, so instead of putting one, one, one, one kg block, I'll put four kg of that stone over there. The piston will suddenly go down, compression takes place and attains this state B. Can do that. So this process is faster than the previous one, right? The movement of piston you can observe. Piston will go down suddenly, right? All of a sudden, correct? This process is irreversible process. It happens fast, right? Against a constant, against a constant external pressure because the moment that you put in this block, heavy block of four kg, external pressure will rise to a certain value and compression takes place because of this new external pressure and that is same throughout the process from this point to this point, isn't it? So can we say here, the piston, sorry, the external pressure is constant? Can we say that? Did you understand? Tell me, did you understand all of you? You know, isobaric is constant pressure process. Okay, whether it is happening too fast or too slow, that's a different thing. Irreversible is different than isobaric. The only thing is common in irreversible and isobaric is constant external pressure, okay? Isobaric can be extremely fast or slow but reversible, irreversible is always fast process. Yeah, it is, see, that's what I'm defining. Try to understand the difference. It's not like four kg block is irreversible. Try to understand the difference in the two process, okay? State A to state B, we are going slowly, that is reversible. One other way is what? All of a sudden you increase the pressure and the pressure will go down to state B. That is one way also, which is faster than the previous one, extremely fast in fact. So this kind of process is irreversible process. Yes, so whatever the change, mother, we have, against that change only, the compression is taking place. It's not like I'm not talking about this pressure. Once you put the block over here, we have some external pressure plus some pressure we are putting in because of this block. So against this pressure, the compression is taking place. So whatever the pressure is, it is same throughout the process, state A to state B. Isn't it? No, we won't say the time is zero. We just say it is faster than the previous process. It happens so fast. Time thing we don't consider here. We don't define this in terms of time, okay? It takes a lot of time and it takes almost zero time, not like that. So did you understand the basic difference between the two process? Yes, this one, quickly guys. Basic difference you understood, correct? So this is why you see the external pressure in case of irreversible processes constant, but is not constant. But in case of reversible process, it is, it varies, right? It variable, constant for irreversible, variable for reversible, okay? So like we have seen some properties of reversible process, we have some properties of irreversible process also. I'm not going to draw the piston cylinder system over here. Just you write down few process and then we'll see the graph of this, okay? So it is first of all unidirectional. You cannot reverse it. That's why it is irreversible, unidirectional. Write down. We cannot reverse the process to the initial position. If you want to reverse it, you have to do some work on it, right? So work has to be done. Work has to be done on system, on system by surroundings, by surroundings to restore system, to restore system in its original position. Without work, it is not possible in its original position. Without work, it is not possible because it is irreversible, okay? Some, because the process is very fast, some amount of heat has been lost, some amount of energy has been lost, you know, in the form of heat. The process is fast, no. So because of friction or, you know, if friction you're not assuming there, if it is frictionless also, because of fast process, some amount of energy is lost in the form of heat. That's why if you remove the block, right? The energy that has gone already, you cannot restore that energy. So original pollution, you won't gain. If you want to gain, you have to provide some energy from outside. That is the work done. Understood? Yeah? So finite, so that's what you see. Fast process, right? There will be exchange of energy with surroundings. Slow process, the process is extremely slow, right? Exchange of energy with surroundings is not possible. That is also a very important point, okay? Next slide down, it has finite number of steps. Finite steps means what? We can count eight, 10, 12 like that. It's not like infinite steps, we cannot count that. So it has finite number of steps, fast process. They ask this in the school exam also, difference between irreversible and reversible process. It is the fast process, okay? It is real and actual one. The actual process is this only. The previous one, if you remember, we have discussed this imaginary, won't happen unpractically. System is at thermodynamic equilibrium. System is at, it's not like we don't have equilibrium over here. But the only difference is at thermodynamic equilibrium, thermodynamic equilibrium, at only initial and final step, initial and final step, at only initial at final step, correct? So we have equilibrium only at initial and final step. And that's why PV is equals to NRT we can apply only at initial and final step, right? On the next point, we can apply PV is equals to NRT, only at initial and final step, okay? And the most important one is we have P external constant, constant external pressures. One second, this copy is done. I'm just coming, I'll take some water and come. Just a second, yeah, copy this. Done? Yes. Done, no? Okay. Now, if you look at the graph here, graph for this process, okay? So we have pressure, volume. External pressure is this initially when state A we have external pressure is this. Now, when you put the block, 4KG block, all of a sudden the pressure will come down, right? It is state B. And in this process, what happens? The expansion takes place, right? And the graph will go like this. Expansion goes like this. Okay, it won't touch the, you know, x axis here. We'll just remove this point, just to make you understand I have taken this graph. So this is a decrease in pressure and in that pressure the expansion takes place like this. So constant pressure, which is this. Against this pressure only the expansion is taking place. So these are the processes you need to understand and keep in mind, okay? No, this is just here to make you understand. It's like pressure was here initially. Once you increase the pressure, it will go down. And then the pressure volume expansion happens. No, so it goes like this. So it's a continuous graph. It's not like it is, you know, coming down and then like this. There's no steps over it's continuous graph like this because both happens, you know, the pressure increases all of a sudden, decreases all of a sudden and then the expansion takes place like this. I have taken this, the example of irreversible expansion. You will show this graph to what they see. It's not like these two points you will show, right? The relation of PV is like this only exponential relation. So you draw the graph like this. The expansion is why the graph stops at this point because it's happening against this pressure. That's why it stops over here. No, PV is goes to NRT is applicable only at this and this point, initial and final. And it's part does not matter over here but it goes like this only. So this is the processes you need to understand, okay? Now next slide down, we'll see thermodynamic quantity. After finishing this thermodynamic quantity, we can think of, you know, the first law of thermodynamics we can start and then we can start the derivation also or work on another things, correct? So first of all, you write down the heading, thermodynamic quantity. First one is work. Work is generally we have PV work we are discussing. Pressure volume work, okay? So for this first of all, we have an IUPAC convention. This you need to memorize, IUPAC convention. And what is this convention? On the system is always positive. Just a second. Work done on the system is always positive. Whenever work is done on the system, it is a case of compression, right? Work done by the system. System is doing work, right? By the system is negative. Remember it is Ulta in physics, okay? It is a case of expansion. So there's no any mistakes over here. This is the convention of we use in chemistry. In physics it is opposite, okay? The work done formula that we have, general formula is DW is equals to minus of P external into DV. This is the general formula we have for all processes. The expression of work done, we always get from this particular formula. Okay, all the processes will just apply the condition of a particular process and we'll get the expression of work done from there, okay? So this is the relation we have. Now in this, if you find out W, so we have to integrate it, V1 to V2 and zero to W, correct? So W is equals to we get minus P external DV V1 to V2. This is the in general expression we have, which we use to find out the expression of work done various process. Yes, understood. The unit of work done is we can have, yeah, unit of work done we can have, Joule we can have Caledee, we can have ATM liter, and we can have, yeah, we can have ATM liter, okay, anything we can have. Whenever you do P into V, so pressure is an ATM, volume is in liter, so mostly you will get the work done in ATM liter. So always keep that in mind. So whenever work done is an ATM liter, you have to convert it in Joule. So one ATM liter, one ATM liter is equals to 101.325 Joule, with this you can easily convert. Or if you don't remember this, you must know that 0.0821 R value, 0.0821 ATM liter per mole Kelvin, right? ATM liter per mole Kelvin, no, no, depends on the option, but I would suggest take this value only. We don't approximate it to zero. And we also know R value 8.314 Joule per mole Kelvin, right? So if you see these two value here, can we write this 0.0821 ATM liter is equals to 8.314 Joule? So from this you can always find out one ATM liter equals to 8.314 divided by 0.0821 Joule. So with this expression also you can find out the relation. Got it? So any one, you know, relation we can keep in mind. So this is the work done thing, right? Now we have few conditions into this and in different, different processes, how to find out work done. Okay, we'll continue with this in the next class. But after next class you can start solving numericals on this. Okay, okay, thank you. Take care.