Figure 23.1

Refer to Figure 23.1. Let a system change from state 1 to state 2 by a reversible process A and return to state 1 by another reversible process B. Then 1A2B1 is a reversible cycle. Therefore, the Clausius inequality gives:

(23.1)

If the system is restored to the initial state 1 from state 2 by an irreversible process C, then 1A2C1 is an irreversible cycle. Then the Clausius inequality gives:

(23.2)

Subtracting (23.2) from (23,1)

(23.3)

Since the process 2B1 is reversible

(23.4)

or,

(23.5)

This can be generalized as

(23.6)

Where the equality sign holds good for a reversible process and the inequality sign holds good for an irreversible process.