Problem 2.11

Find the maximum attainable temperature of ideal gas in each of the following processes: (a) $p=p_{0}-\alpha V^{2}$ (b) $p=p_{0} \mathrm{e}^{-\beta V}$ where $p_{0}, \alpha$ and $\beta$ are positive constants, and $V$ is the volume of one mole of gas.

T_{\max }=2 / 3\left(p_{0} / R\right) \sqrt{p_{0} / 3 \alpha}

Equation of the gas state processes