Entropy Change of Ideal Gas

Unit-3

AVAILABILITY AND APPLICATIONS OF II LAW

Ideal gases undergoing different processes - principle of increase in entropy. Applications of II Law. High and low- grade energy. Availability and Irreversibility for open and closed system processes - I and II law Efficiency

1. ENTROPY CHANGE OF IDEAL GAS

Consider an ideal gas heated from state 1 to state 2 and thus, the temperature is increased from T1 to T2 as shown in Figure 3.1.

During the heating process, there should be some change in entropy in the gas. If a change in heat transfer dQ is considered to the gas at an absolute temperature T, then the change in entropy is given by ds = dQ / T.

1. Expression for Change in Entropy of Ideal Gas

(i) In terms of temperature and volume:

By the law of conservation of energy or first law of thermodynamics,

Dividing equation (3.1) throughout by 'T',

Integrating above equation from state 1 to state 2,

(ii) In terms of pressure and temperature:

By gas equation,

Substituting (3.3) in (3.2) change in entropy,

Also, it can be written as

(iii) In terms of pressure and volume by gas equation:

Substituting this value in equation (3.2) change in entropy,