The TS diagram below shows two internally reversible cycles

The T-S diagram below shows two internally reversible cycles. The 1-A-2B-1 cycle is formed by the internally reversible processes A and B. On the other hand, the 1-A-2-C-1 is formed by the internally reversible processes A and C. In fact, B and C are two arbitrary internally reversible processes connecting to equilibrium states, 1 and 2. Based on this information, show that the integrals for paths 2B-1 and 2C-1 are equal; that is,

Solution

Since, it is a path function hence the quantities are equal.