Calculation of Entropy Change

The following facts should be kept in mind while calculating the change in entropy for a process

1. for a reversible process
2. Entropy is a state function. The entropy change of a system is determined by its initial and final states only, irrespective of how the system has changed its state.
3. In analyzing irreversible proceses, it is not necessary to make a direct analysis of the actual process. One can substitute the actual process by a reversible process connecting the final state to the initial state, and the entropy change for the imaginary reversible process can be evaluated.

Entropy change for some elementary processes

1. Absorption of energy by a constant temperature reservoir

A certain amount of heat is added to a constant temperature reservoir. The actual process can be replaced by a reversible path in which an equivalent amount of energy is added to the reservoir. Then, the entropy change of the reservoir is given by

(22.6)

2. Heating or Cooling of matter

The heating can be carried out either at constant pressure or at constant volume. From the first law of thermodynamics

for constant volume heating/cooling process

for constant pressure heating/cooling process

, for a constant pressure process

(22.7)

or,

, for a constant pressure process

(22.8)

Similarly,

, for a constant volume process

(22.9)

or,

ln , for a constant volume process

(22.10)