Problem 2.50

One mole of an ideal gas whose adiabatic exponent equals $\gamma$ undergoes a process in which the gas pressure relates to the tem perature as $p=a T^{\alpha},$ where $a$ and $\alpha$ are constants. Find: (a) the work performed by the gas if its temperature gets an increment $\Delta T$ (b) the molar heat capacity of the gas in this process; at what value of $\alpha$ will the heat capacity be negative?