1.17.1: Isentropic
The term ‘adiabatic’ means that for a closed system no heat passes between system and surroundings; \(\mathrm{q} = 0\). The term ‘isentropic’ introduces the further constraint that the system remains at equilibrium with the surroundings; i.e. the affinity for spontaneous change is zero. From the Second Law,
\[\mathrm{T} \, \mathrm{dS}=\mathrm{q}+\mathrm{A} \, \mathrm{d} \xi \quad \text { where } \mathrm{A} \, \mathrm{d} \xi \geq 0 \nonumber \]
The isentropic condition means that both \(\mathrm{A}\) and \(\mathrm{q}\) are zero. Hence \(\mathrm{dS}\) is zero, indicating that the entropy of the system remains constant. In other words, ‘isentropic’ describes an adiabatic change along an equilibrium and therefore reversible pathway.