 Welcome back. We now know that a 2T heat engine between two different temperatures T1 and T2 will work only in one way. If we can set up an engine which absorbs heat from T1 and rejects it to T2, then we will not be able to set up a 2T heat engine which absorbs heat from T2 and rejects heat to T1. What does this have to do with flow of heat only in one direction? Let us try. Let us say that we have a 2T heat engine working between T1 and T2 absorbs Q1 from the reservoir at T1, rejects Q2 to the reservoir at T2 and produces work which is positive. This is given. Now the question is, suppose I have these two reservoirs at two distinct temperatures. I should consciously write it down to emphasize that the two temperatures are different. I allow direct contact between them through a device, maybe a conducting rod or something which allows flow of heat. Since the two temperatures are different, the two systems, the one system, the reservoir at T1 and another at reservoir at T2 are not isothermal systems. And hence, if we connect them via a diathermic wall, that means allow them to come in contact with each other in which direction will the heat flow. There are two possibilities. Heat will flow from T1 to T2. Let us say this is possibility A. Another possibility is heat will flow from T2 to T1. Let us say this is some QA. Another possibility is B and heat QB may flow from T2 to T1. Which one is possible and which one is not possible? We know from the general observation of nature that heat will flow only in one direction. If two systems have states such that heat flows from say system 1 to system 2, it will not flow from system 2 to system 1 if their states are not changed. We say if their temperatures are unchanged. The trick is the same. Combine our proposal with the given two T heat engine and see whether it leads to an inconsistency. An inconsistency for us is setting up a device which highlights the Kelvin-Planck statement of the second law of thermodynamics. Let us consider the first possibility. We will say E and A. What happens here? We have T1, we have T2, we have our engine E as given. And in addition, we have some heat being transferred through this second possibility. And the way the direction is shown here, QA from T1 to T2 is greater than 0. So, QB also from T2 to T1 greater than 0. Just now we are considering the combination E and A. And you will notice that even if you combine these two processes, we still have a proper two T heat engine because all that happens is because Q1 is positive and QA is also positive. Well, this is equivalent to something like this T1, T2. This will be our E and the process A. All that it does, it absorbs Q1 plus QA. It rejects Q2 plus QA and produces the same amount of work as earlier. So, in this case, there is no inconsistency. Now, let us consider the other combination. Let us consider E and B. And let us see what happens. E and B means we have the two reservoirs T1 and T2. And it is given to us that an engine is working between them as before. Now, B means we have a facility by which an amount of heat QB is transferred from the reservoir at T2 to the reservoir at T1 in this direction. Now, let us see what happens. Notice that the engine E is rejecting heat to the reservoir at T2. And this process B is extracting some heat from T2 and providing it back to T1. So, let us adjust QB or QB and Q2 such that QB equals Q2. So, now let us see what happens. Let us sketch the whole thing again. We have this reservoir T1. It is providing to our engine E heat equal to Q1 and the engine E is producing work W greater than 0. The engine E is rejecting heat Q2 to the reservoir at T2. But the T2 says that look I do not really have to receive it because Q2 is now equal to QB and the reservoir at T2 is providing Q2 equal to QB back to reservoir at T1. Now, let us consider this as E plus. Now, notice that this is equivalent to an engine a cyclic device because B does not produce any change in any system. So, this is E and B. It produces a positive amount of work and it absorbs heat equal to Q1 minus Q2 and since Q2 is less than Q1 remember E is an engine. This will be a positive number. So, this is one thing which violates the Kelvin Planck statement and what does this mean? This means that such a combination cannot exist and that means given T1 T2 such that T1 is not equal to T2 heat may flow only in one direction.