The last equation provides a direct expression for computing entropy change between two states for an ideal gas.
For the special case of a reversible adiabatic dQ = 0; hence dS= 0. Thus:
For constant , it follows that:
(4.22)
One may note that eqn. 4.22 provides the same relation as obtained by the Fist Law analysis as in eqn. 3.18.