21.11 : Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.

The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram. Then, break the cyclic integral into two parts. By reversing the integral along one path, which is feasible because entropy change is defined for any reversible process, it is shown that the total change in entropy is independent of the path. That is, entropy is a state function.

The statement implies that a unique value of the entropy can describe a system under consideration. Note, however, that the absolute value of entropy is not defined, as the definition gives only the entropy change. Once a reference value of entropy is defined for a particular state of the system, then the absolute value can be obtained for all other states.

Irreversible processes lead to a change in entropy more than reversible processes, thus changing the state of a system differently. Thus, an irreversible cycle leads to a net increase in the entropy of a system and its surroundings. This observation leads to the entropy statement of the second law of thermodynamics.