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 \(V=V_{0}\).