 Welcome back. Now, let us ask ourselves the following question. We have two reservoirs at two distinct temperatures T1 and T2. T1 is definitely not equal to T2. So, we have a two T heat engine. And let us say that the engine works by absorbing Q1 from the reservoir at T1, rejecting Q2 to the reservoir at T2 and producing a positive work output. The question is if this works, then let us consider a situation where we have the same reservoirs. And now let us see whether we can have an engine say E prime which will produce work say W prime. Instead of absorbing from the reservoir at T1, let it absorb Q2 prime from the reservoir at T2 and Q1 prime be rejected to the reservoir at T1. So, the question we are asking ourselves is if an engine, two T heat engine works like this, can we have another two T heat engine working in a sort of different way? Will such an engine E prime will also be possible? Notice the difference. Here the heat is absorbed from the reservoir at T1 whereas heat is absorbed from the reservoir at T2. Here heat is rejected to the reservoir at T2. Here heat is rejected to the reservoir at T1. So, the source and sink are interchanged for the two engines. Now what we do here is the following. We always check whether this combination will violate the Kelvin-Planck statement of the second law. That means can we set up a one T heat engine using this combination? If we can set up a one T heat engine, that means we are violating the Kelvin-Planck statement and that means the second assumption which we made that engine E is working as well as engine E prime is working. The second statement that the engine E prime is working will obviously be false. Let us see whether we can do that. What we do is we say let Q2 prime be adjusted in such a way that Q2 prime equals Q2. Remember that we assume that all our interactions are continuous and are scale independent. So I can always scale this engine up or down as required to adjust Q2 prime equal to the Q2 of the first engine E. And obviously W prime and Q1 prime will automatically get adjusted as required when Q2 prime is adjusted equal to Q2. Now let us set up our T2 in such a way that all that it does is absorb Q2 from this engine E and reject it or provide it to this engine E prime. Let me re-sketch it like this. So I will draw a big reservoir T1. What it is doing is providing heat Q1 to our engine E. Engine E produces W greater than 0. Engine E provides Q2 to this reservoir at T2. But T2 says I do not really have to keep it with me because Q2 prime equal to Q2 is now being made available to the engine E prime. So the reservoir T2 just says that the temperature here is T2. Otherwise the reservoir T2 neither gains nor loses any amount of energy in the form of heat. It essentially goes out of the picture. Now what does E prime do? E prime produces a positive amount of work W prime greater than 0 and it rejects to this reservoir at T1 heat equal to Q1 prime. Now let us see the consequence of this. First W is greater than 0. Consequently Q2 will be less than Q1. Why? Because W is Q1 minus Q2. If W is positive Q2 has to be less than Q1. Now here Q2 prime equals Q2. So we have Q2 prime less than Q1. Now some positive work is extracted and we will have by the first law. Remember E prime is also a cyclic device. Q2 prime equals Q1 prime plus W prime. And since W prime is positive Q1 prime will be less than Q2 prime and hence we will have Q1 prime less than Q2 prime which has been showed to be less than Q1. Now consider the whole of this as an engine, combined engine E and E prime put together. It is a cyclic device because E is a cyclic device, E prime is a cyclic device and T2 does not come into picture because it receives no net heat. Now what does it do? This is equivalent to an engine E and E prime absorbing heat equal to Q1 minus Q1 prime from this reservoir at T1 and producing a positive work output which is W plus W prime. Since both of these are positive, the sum is also positive and we have shown that Q1 minus Q1 prime, Q1 is greater than Q1 prime. So this one also is greater than 0. So that means this is equivalent to a 1T heat engine. Now what does this mean? This means that such a combination would violate the Kelvin Planck statement of the second law. That means it directly violates the second law of thermodynamics and this implies that if an engine works as T1, T2 and T1 not equal to T2, then we cannot have an engine like this. And what is that engine like this? It is an engine which works between the same two reservoirs but absorbs from T2, rejects to Q1 and produces W prime greater than 0. So if this is true, this is not true. That means this implies that given two reservoirs T1, T2 such that T1 is not equal to T2, a 2T heat engine will work only in one way. It will work like this and not like this or if you insist that it will work like this, it will not work like this. Thank you.