For reversible adiabatic process, change in entropy is

Explanation:

Adiabatic process: 

When a thermodynamic system undergoes a change in such a way that no exchange of heat takes place between the system and surrounding, the process is known as an adiabatic process.

ΔQ = 0

Entropy (S): 

It is a measure of the disorder of the molecular motion of a system.

Greater is the disorder, greater is the entropy.

The change in entropy is,

\({\rm{\Delta }}S = \frac{{{\rm{\Delta }}Q}}{T}\)

where, ΔQ = heat exchange, T = temperature of the system.

For a reversible adiabatic process

\(dS = \frac{{dQ}}{T} = 0\)

Entropy remains constant in an adiabatic process which is also reversible.

For the sake of simplicity consider the case of a closed system, i.e. a control mass, which does not exchange any mass with the surroundings.

There are two ways in which the entropy of such a system can change, firstly through heat transfer at the system boundary and secondly through entropy generation inside the system.

Now the process is adiabatic, so the heat transfer is zero and so the entropy change is zero through heat transfer.

Also, the process is reversible, so there is no entropy generated inside the system and the entropy change due to entropy generation is zero.

In this way, the entropy change is zero for an adiabatic process which is also reversible.