Problem 2.146

One mole of an ideal gas with heat capacity \(C_{V}\) goes through a process in which its entropy \(S\) depends on \(T\) as \(S=\alpha / T,\) where \(\alpha\) is a constant. The gas temperature varies from \(T_{1}\) to \(T_{2} .\) Find: (a) the molar heat capacity of the gas as a function of its temperature; (b) the amount of heat transferred to the gas; (c) the work performed by the gas.