1. Entropy change in an irreversible process
For any process undergone by a system, we have
(or)

2. For any reversible cycle 1-A-2-B-1, we have
For any reversible cycle 1-A-2-C-1, we have from Clausius inequality, A C
Combining the above two equations, we have B C B C
(or)

3. Since path B is reversible,
Since entropy is a property, the change in entropy is same for the paths B and C between the same limits 1 and 2 C
Therefore, from the above equations, we have
Thus, for any irreversible process,
and, for any reversible process,

4. Entropy principle
For any infinitesimal process undergone by a system, we have
For an isolated system which does not undergo any energy interaction with its surroundings, we have
Therefore for an isolated system,
Thus, for any reversible process,
(or)
and, for any reversible process,
Thus, the “entropy of an isolated system can never decrease”. It is called principle of increase of entropy (or) entropy principle

5. Entropy principle
Thus, the “entropy of an isolated system can never decrease”.
It is called principle of increase of entropy (or) entropy principle.
The entropy of an isolated system always increases and becomes a maximum at the state of equilibrium.