 Hello, guys. Good evening. Can you hear me? Okay, so what have we done last class? Well, I think work done expression we have done, right? Yeah, okay. Okay, so we have done the numerical on delta H relation. So we haven't done the graph comparison visit. Have you done graph comparison of isothermal and adiabatic process? Yeah. Okay, so write down the comparison of comparison of graph in adiabatic and isothermal process. Okay, one second. Yeah, so we had discussed this isothermal process and we know the relation of relation of PV in isothermal process is equals to PV is equals to constant. Right, PV is equals to constant. So if you look at the graph over here, the graph of pressure and volume, suppose the y axis is P and x axis is V. Okay, so the graph here is like this pressure and volume graph. Okay, the slope of this graph, if you try to find out so we need to find out dp by dp. dp by dv is the slope, right? Why the slope? You know, if you draw the graph of like if you have a graph of y and x axis, y and x axis, the slope is what? It is dy by dx. Correct? The slope is dy by dx. Similarly, we have P and V graph over here. So the slope would be dp by dv. So you need to find out this dp by dv. So what is dp by dv? You see this relation we have will differentiate it. So dp by dv is equals to suppose I'm assuming a constant k over here. This would be minus k times 1 by V square, right? So this is the slope of, slope of isothermal process, isothermal process minus k times 1 by V square, isn't it? Any doubt in this? Like if you differentiate this, you'll get this only. Yes? Yeah. So this slope, just this expression you keep in mind. Now you see the expression in adiabatic process. What is the relation of P and V in adiabatic process, could you tell me? The relation of P and V here is, last class we have discussed, it is P V to the power gamma is equals to constant. Constant k suppose we have. And this gamma is always greater than 1, isn't it? Gamma is always greater than 1 for all gases, monotomic, diatomic and polyatomic gases, always greater than 1. What is the value of gamma for monotomic gas, could you tell me? It is what? Is it 3 by 5 or 5 by 3? Yeah, it's 5 by 3, 1.66, always greater than 1, right? If you talk about diatomic, it is 1.40 and for polyatomic, it is 1.33, right? So this is the value of gamma for different types of gases. Right? So obviously this gamma value is greater than 1 over here. If you look at the expression of isothermal, it is P V to the power 1 is equals to constant. You can write this with isothermal. But for adiabatic, it is P V to the power 1.7, depending upon the nature of the gas. So basically gamma will write down here. Means what the power of V is greater than 1 we have over here, okay? So if you draw the graph of P V in adiabatic process, graph of P V in adiabatic process, you will get like this. This is pressure and this is volume. This is pressure and this is volume. So here also the nature of graph is this, right? So nature wise you see both graphs looks like similar. Yes. Could you tell me the slope of this graph dp by dv of adiabatic process? Could you tell me the slope? Yes, what it is? Gamma K V to the power gamma plus 1, is it? Okay, wait. If you differentiate this, what we get with respect to V, right? So P is constant. So we'll take this P out and the differentiation would be minus gamma V to the power minus gamma minus 1. This is what we get. The differentiation of 1 by V to the power gamma is this, which further you can write. We have constant also we have over here, that is K. So this is equals to, why did I write P over here? This won't be there because P is what you see? P is what? K by V to the power gamma, you differentiate, you'll get this. So minus gamma V to the power gamma plus 1 into K is P V to the power gamma. So V to the power gamma, V to the power gamma will get cancelled. So minus gamma into P by V we have. So what is minus P by V? Could you tell me? Gamma into minus P by V. If you look at the previous expression of slope, right? Adiabatic DP by DV for adiabatic process, the slope is this, slope is this, which this minus P by V is what? Minus P by V is the slope of isothermal process, right? So what we can write here? Next, we can write the slope of adiabatic process, yeah. The slope of adiabatic process, which is DP by DV of adiabatic is equals to gamma times DP by DV of isothermal. So what can we conclude? The slope in adiabatic process is gamma times more than the slope in isothermal process. Okay, copy this down just a second. Yeah, copy this. Clear? Okay. This is one thing that you must keep in mind. So if you draw the graph over here, graph of both adiabatic and isothermal process, suppose you're drawing like this, right? Two graphs we can draw. Yeah. The two graphs, if you draw here, you see, this is one. This is another one, right? Two graph you have drawn. Now, you need to first identify which graph is for adiabatic and which graph is for isothermal. Correct, adiabatic or isothermal. Expansion we are considering means the volume is increasing. So obviously the slope is more for adiabatic process, right? So the steeper curve that you have is adiabatic. Correct. So this graph, the graph which is below is adiabatic steeper curve and which is above here, it is isothermal. Like this we identified, PV graph, right? So the steeper curve is adiabatic. Okay, copy this down. Yeah. So look at these two conditions here. Remember the graph that I have drawn in the previous slide, it was for expansion. Okay, the volume is increasing. Keep that in mind. Okay, two cases we have here, when expansion is taking place, right? So I'm considering overall order is expansion, overall order is expansion, right? And in this, the first case we are assuming, if final pressure is same, if final pressure is same, final pressure is same. And the second condition we have, when final volume is same, right? Two graph I'm drawing here, you see. So this is pressure, expansion we have over here, right? Final pressure you see in both the process, final pressure is same. That is what the condition we have. So when there is an expansion, so the lower graph is always adiabatic, that you keep in mind. Logically also we can understand this. This graph is adiabatic, and this graph is isothermal, more steeper curve, right? This is for final pressure. If final volume is same, see here, if final volume is same, so we have expansion, so final volume is same, the curve could be like this. See the final volume is same. It is VF, volume axis, pressure, this is the expansion, so volume is increasing. So in this case also, like I said, the lower graph is adiabatic, the lower one is adiabatic, and the upper one is isothermal. One more thing you must keep in mind, note all of you write down, isothermal curve never intersects, never intersects each other. Like you see, if you try to draw the curve, isothermal curve at different temperature, then the graph will never intersect. At one temperature we have like this, another temperature we have parallel like this, like this is parallel. This graph will never intersects. If it is given in the question, like you see, the question here is like this, suppose the last one I have shown, let me show you. Suppose this graph is given, and the question is which one is for adiabatic and which one is for isothermal, like this, okay? So you can easily identify, obviously in the question it is written that whether the curve is adiabatic or isothermal is a question like this. And since the curve is intersecting at a point, so both cannot be isothermal curve. Right, means we can talk about that these two curves are isothermal at different different temperature. But since they are interacting or intersecting at a point, hence both curve cannot be isothermal, okay? They can be adiabatic but not isothermal is not possible, right? So this is the two case you must keep in mind, lower graph is isothermal, sorry adiabatic and upper one is isothermal. Now you see one thing more. Suppose you have to compare the work done in isothermal and adiabatic process, where we'll have more work done in isothermal or adiabatic, which process gives us more work done? Why adiabatic and why isothermal? Okay, you see this. If you have PV graph given, then what is the work done? PV graph given, what is the volume of work done? What is the work done in PV graph? That is the area under the curve, right? Yeah, that's fine, area under the curve. So suppose we have graph like this, let me draw this graph this way. We have pressure volume graph. So this is pressure, this is volume, pressure volume graph. And the two graphs will have like this. So it was constant volume. So obviously this graph is adiabatic and this graph is isothermal. Final pressure is this obviously, this is VF and this was VI. So since this curve is adiabatic, so if I ask you, work done in adiabatic process, your answer would be what? Your answer would be this curve, area under this curve, isn't it? Whatever the area we have, that would be the work done. Obviously like this, since we have a curve over here, you don't have to find out the area, but you can easily understand whether it is more or less. Okay, but if it is for isothermal, we know this curve, the upper one, expansion we have, so upper one is isothermal. And the work done in isothermal process would be area under this curve, which includes this area as well. You have to include this area. Obviously, the area in isothermal process is greater than the area in adiabatic process. That's why what we can conclude the work done in isothermal expansion is more than the work done in adiabatic expansion, expansion process. Clear understood? Isothermal process will have more work done. Can I go to the next slide? Copy all of you? Yeah. Now the second case we have in this, that is a case of compression. Again, in this, I am assuming two cases here. One is when final pressure is same, is same. And the second one, when final volume is same. In this, the things will be opposite. When final pressure is same, it is a case of compression. This is the compression process we have. Just a second. This is PF pressure axis, compression. So volume is decreasing. And this is volume. Again, P and V. Final volume is same. The graph goes like this. Final volume is this. VF compression. Correct. So obviously you see here, here the things will be opposite. In the last case, the lower graph is adiabatic. But here the lower one would be isothermal. And the upper one would be adiabatic. This is also isothermal. And this one is, this property you must remember. Graph related questions they ask on this. Now on this only you see, after all this discussion, you see what questions they have asked once in JXM. Look at this question. Look at this graph first. Pressure volume axis we have. Three graphs are drawn. One. Then we have two. Three graphs are drawn like this. One. Two. And three. Okay. You need to find out which graph is for, is for mono atomic gas. Which graph is for diatomic gas. And which graph is for polyatomic gas. Could you tell me this? Try once. It is a case of expansion we have here. Expansion. It's not triatomic Rohan. We can say it is polyatomic. Okay. Now the answer for this question is monoatomic gas is graph three. Two. And polyatomic is graph one. Okay. Why? Because you see this graph from this, you will understand. You see this graph. This is for isothermal. So for this graph, what we can write PV is equals to constant. And for this graph, it is PV to the power gamma is equals to constant. Expansion. Okay. So what we can say here. As the power of V is increasing. Okay. As the power of V is increasing. From one to 1.6 or four or three, whatever. Power of V is increasing. The graph is shifting down. Right. So as the value of gamma increases, the graph shifts down. That is what we can conclude. Right. As the value of gamma increases, the graph shifts down. Okay. Now this logic, if you apply over here. In this particular question. So this one will have this graph will have the first one. We'll have the minimum gamma value. Because it is on the tops of minimum gamma. And this one will have the maximum gamma value. Because as we go down, the gamma value increases. So maximum gamma. Means it is poly atomic. Hence the orders. Any doubt. Tell me, did you get it? Compression. If you go back. Right. Below one is isothermal upper one is ideal. So it will be. Yes. Yes. Yes. Tell me. I have understood. This question. All of you have understood. Yes. So this is the first, you know, a portion of this chapter that is thermodynamics. Okay. Thermodynamics has two parts. The first part is done over here. With this graph comparison. The first part is done.