GITAM, Department of Engineering Physics

Entropy and the second law

Statement: A natural process that starts in one equilibrium state and ends in another will go in the direction that follows the entropy of the system plus environment to increase.

This statement of the second law is consistent with the Kelvin-Planck statement and also with the Claussius statement.

Proof: according to Kelvin-Planck statement of second law, there cannot be a perfect heat engine which may convert all the heat Q taken from the source at temperature T into work. If it were so, the entropy of the source would decrease by Q/T, whereas, that of the working substance would remain unaltered, because it returns to initial state after completing the cycle. Thus the entropy of the system plus surrounding would decrease, which is against the principle of increase of entropy.

In the same way, according to Claussius statement of second law, there cannot be a perfect refrigerator, which, unaided by an external agency, may transfer heat Q from a cold body at temperature T2 to a hot body at temperature T1. If it were so, the entropy of cold body would decrease by Q/T2, and that of hot body would increase by Q/T1, and that of working substance would remain unchanged. Since T2 < T1, the total entropy of the system plus surrounding would decrease by Q/T2 – Q/T1, which is against the entropy principle, because the entropy of a thermodynamic system plus surrounding either remains constant or increases  but can never decrease.

Thus the principle of entropy is consistent with both the Kelvin-Planck and Claussius statements of second law of thermodynamics.