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.