All Problems First law of thermodynamics, heat capacity
Problem 2.52
An ideal gas has a molar heat capacity \(C_{V}\) at constant volume. Find the molar heat capacity of this gas as a function of its volume \(V,\) if the gas undergoes the following process: (a) \(T=T_{0} \mathrm{e}^{\alpha \mathrm{V}}\) (b) \(p=p_{0} \mathrm{e}^{\alpha V}\), where \(T_{0}, p_{0},\) and \(\alpha\) are constants.
2.52. (a) \(C=C_{V}+R / \alpha V\) (b) \(C=C_{V}+R /(1+\alpha V)\)