 Welcome back. Now it is time for us to associate an engine with one or more reservoirs. Let us try to create an engine which is working with only one thermal energy reservoir and let us see the consequences. Because we are now trying to associate an engine with a single thermal reservoir, we will give it the nomenclature 1 T heat engine indicating that we have a heat engine and it is associated only with one thermal energy reservoir at some fixed temperature say T1. So the scheme would look like this, we have a reservoir at T1 and we have an engine E. The engine has to produce net work output greater than 0, otherwise it would not be an engine and it has to absorb some amount of work say Q in and it has to absorb some amount of heat say Q in from this single thermal energy reservoir at temperature T1. Now what is the consequence of this? Because there is only one thermal energy reservoir which just supplies heat to the engine E, the efficiency of this engine which is defined as W net by heat supplied. Now heat supplied by first law will be equal to Q in and by first law it will be equal to W net. So that means this is going to be equal to 1 and that means such an engine is not possible because of the Kelvin Planck statement of the second law of thermodynamics. It violates the Kelvin Planck statement. So we say 1 T heat engine cannot be set up. You may beat one but it will never work. What about a 2 T heat engine? Let us try. Now since there are two reservoirs, we have two choices. The engine can absorb heat from both the reservoirs or the engine can absorb heat from one reservoir and reject heat to the other reservoir. The third option that the engine rejecting heat to both the reservoirs it just not possible because if it is only rejecting heat not absorbing any heat then it would not be able to do any work and it will not be an engine anyway. So there are only two options possible for a 2 T heat engine either absorb heat from each of the two reservoirs or absorb from one and reject to the other. Let us look at the first option. In the first option we have two reservoirs and an engine E producing work W net absorbing heat from each of the two reservoirs. Let us say it absorbs from a reservoir at temperature T1 heat equal to Q1 and the reservoir at temperature T2 provides heat to the engine which it say Q2. Now look at the consequences. This is heat absorbed, this is also heat absorbed, this is work done. So the first law becomes because the engine is a cyclic device W net is Q1 plus Q2. What is the heat supplied? Heat supplied is heat absorbed, heat supplied is also Q1 plus Q2 and that means the efficiency of such an engine which would be W net by Q supplied which will be equal to 1 and that means this is a violation of the second law as stated by the Kelvin Planck statement. Hence such an engine cannot be set up and that means we must forget about the idea that the engine absorbs heat from one reservoir and also absorbs heat from the second reservoir. Let us look at the second option. Let us now look at the other option. Now we say let us have one reservoir at some temperature T1, another reservoir at some temperature T2 and this is our engine. But now it absorbs heat Q1 from the reservoir at T1 and rejects heat Q2 to the reservoir at temperature T2 and of course it is an engine. So it has to produce net work output which is greater than 0. Now what are the consequences of this? Let us apply first law. W net now would be equal to Q1 minus Q2 and since this is greater than 0 we can say that in magnitude Q1 would be greater than Q2. This Q1 is the heat absorbed by our system which is the engine and this Q2 is the heat rejected by our system to the reservoir at T2 and hence Q1 is greater than Q2 because the difference must be W net which E being an engine must be greater than 0. What about the efficiency? Remember that the heat supplied is Q1, the absorbed part. This is not heat supplied, this is heat rejected. So the efficiency would be equal to W net by Q supply which would be W net by Q1 and hence this will be less than 1 and obviously since it is less than 1 we can say that such an engine does not violate the second law and that means we can set up and design and operate such an engine and indeed in real world we have never come across a 1 T heat engine or even a 2 T heat engine which absorbs heat from either just one reservoir or more than one reservoir does not reject any heat and all heat it absorbs converts into work. We have never seen such an engine but we have seen a large number of engines all over engines whether in a car, whether in a train, whether in an aircraft, whether on a ship all engines have this character. It absorbs heat from one or more reservoirs, it rejects heat to at least one reservoir if not more than one reservoir enough for this time till we meet again. Thank you.