Again,

T dS = dQ = 0

1.33

∴dS ≥ 0

1.34

Isolated system does not undergo any energy interaction with the surroundings (dQ = 0).

∴dSiso ≥ 0

1.35

For a reversible process,

dSiso = 0

1.36

or,

S = Constant

1.37

For irreversible or natural process

dSiso > 0

1.38

Hence, entropy of an isolated system can never decrease. It always increases and remains constant only when the process is reversible. This is known as principle of entropy increase or simply entropy principle .

For isolated system,

dSuniv ≥ 0

1.39

or,

dSsys + dSsur ≥ 0

1.40

Fig. 1.15 Equilibrium state of an isolated system