Problem 2.139

One mole of an ideal gas goes through a process in which the entropy of the gas changes with temperature $T$ as $S=a T$ $+C_{V} \ln T,$ where $a$ is a positive constant, $C_{V}$ is the molar heat capacity of this gas at constant volume. Find the volume dependence of the gas temperature in this process if $T=T_{0}$ at $V=V_{0}$.