 Welcome back. Continuing our discussion on reversible processes. Now let us extend it to a cycle. So although we have defined reversible processes in a similar manner, if the reversible process is a cycle, then we can define reversible cycles and since engines and refrigerators work using cyclic devices, suppose we set up an engine which works in a cycle but that cycle is a reversible cycle, then we will end up with a reversible engine and we can then have a reversible refrigerator. In fact, a reversible engine when run in the reverse direction because it is possible to run will run as a reversible refrigerator and vice versa. A refrigerator if implemented as a reversible refrigerator can be reversed and then it will run as an engine. So look at the consequence of this. Suppose I have a reversible engine. It works between two reservoirs T1 greater than T2 and let us say that the engine let me call it now R in, same reversible engine. It absorbs heat Q1 from the reservoir at T1, rejects heat Q2 to the reservoir at T2 and produces work W. And let me put the direction like this clockwise just indicating that it is running in a particular direction. Now if it were a reversible engine, let me show the reverse engine in red color and just to indicate that it is running in the reverse, I will trace it again and put the arrow in the other direction. Just to indicating that now it is not just reversed engine but an engine which has been reversed in its operation. What will it do? It will absorb heat Q2 from the low temperature system, reject heat Q1 to the high temperature system and absorb work W. And that means such an engine if I make it execute one cycle as an engine and then one cycle as a refrigerator by reversing its operation. Then what will happen? The reservoir at T1 would have supplied Q1 to the engine. In the next part it would have absorbed Q1 from the engine reverse which is running as a refrigerator. Similarly the reservoir at T2 would have received Q2 from the engine and provided Q2 to the refrigerator and in the first part the engine would have provided work W. In the next part it would have absorbed the work W. So such an engine when reversed and suppose we executed in one cycle as an engine and another cycle as a refrigerator would leave absolutely no trace. An observer who was not present during this operation of one cycle as an engine and one cycle as an engine would find it impossible to determine whether the one forward and one cycle were reversed or not because no trace would remain on the engine, no work would have been produced because whatever work was produced by the engine was absorbed by the refrigerator and the two reservoirs would also have no trace left because there was no net receipt or withdrawal of heat from any of them. The same thing is true for a refrigerator. So this characteristic is something which we will use now to state and prove the Carnot theorem that will be our next step. Thank you.