Applications of Change in Entropy for different processes

APPLICATIONS OF CHANGE IN ENTROPY FOR DIFFERENT PROCESSES

(a) Constant volume process:

A system undergoing a change of state from 1 to 2 at a constant volume process is shown in p-V and T-s diagram of Figure 3.2.

From equation (3.2), the change in entropy is given by

But in constant volume process,

For constant volume process,

(b) Constant pressure process:

A system undergoing a change of state from 1 to 2 at a constant pressure process is shown in p-V and T-s diagrams of Figure 3.3.

From equation (3.2),

For constant pressure process,

(c) Constant temperature process:

A system undergoing a change of state from 1 to 2 at constant temperature process is shown in p-V and T-s diagrams of Figure 3.4.

From equation (3.2),

Multiplying and dividing by 'T' on right hand side,

(d) Reversible adiabatic or isentropic process:

Adiabatic process is the process in which the heat is neither received nor rejected. So, there is no heat transfer during the process. p-V and T-s diagrams are shown in Figure 3.5.

Note:

(i) There is no area under T-s diagram because there is no heat transfer.

(ii) Since there is no heat transfer during the process, the change in entropy is zero (dS = 0).

(e) Polytropic process:

During polytropic process, there is a heat transfer between a system and its surrounding. There will always be a change in specific entropy. p-V and T-s diagrams for polytropic process are shown in Figure 3.6.

We know that from equation (3.2),

Change in entropy is calculated by using equation (3.2), (3.8) and (3.7).

Another expression may be derived as follows:

Heat transfer during polytropic process is given by

Dividing by 'T' on both sides,

Integrating both sides from initial to final stage,

The equation (3.10) is one form of change in entropy. It can be deduced in other way also.