Problem 2.48

An ideal gas whose adiabatic exponent equals $\gamma$ is expanded according to the law $p=\alpha V,$ where $\alpha$ is a constant. The initial volume of the gas is equal to $V_{0}$ . As a result of expansion the volume increases $\eta$ times. Find: (a) the increment of the internal energy of the gas; (b) the work performed by the gas; (c) the molar heat capacity of the gas in the process.

\text { (a) } \Delta U=\alpha V_{0}^{2}\left(\eta^{2}-1\right) /(\gamma-1) \text { (b) } A=1 / 2 \alpha V_{0}^{2}\left(\eta^{2}-1\right) \text { (c) } C=1 / 2 R(\gamma+1) /(\gamma-1)

First law of thermodynamics, heat capacity