Principle of Increase of Entropy

PRINCIPLE OF INCREASE OF ENTROPY

The change of entropy for reversible process is given by the expression,

ds = dQ / T

Now, the change in entropy is examined for an irreversible process.

Let a thermodynamics system undergoes a change of state from 1 to 2 by a reversible process 1- A-2 and returns to state 1 either by an internally reversible process 2-B-1 or by an irreversible process 2-C-1 shown in Figure 3.7.

For reversible cycle 1-A-2-B-1, the same equation (2.30) can be used.

For irreversible cycle 1-A-2-C-1, Clausius inequality is applied as follows.

Subtracting the equation (3.11) from equation (3.12),

On reversing the limit and rearranging the equation (3.13),

Since, the process 2-B-1 is reversible,

ds = dQ / T

Substituting this value in equation (3.14),

where the equality sign refers to the reversible process and inequality sign refers to the irreversible process.

From equation (3.15), the effect of irreversibility is always to increase the entropy of the system. From this equation, the entropy of a system increases when the heat is supplied to the system.

The principle of increase of entropy states that the entropy of an isolated system never decreases. So, it will be ds ≥ 0 for an isolated system.

Simply,

ds = 0 for the reversible process

ds > 0 for the irreversible process

ds < 0 for the impossible process.