2. An ideal gas undergoes a 'polytropic' process characterized by $pV^m = C$, where $m$, $C$ are constants, from the initial state ($p_1, V_1$) to the final state ($p_2, V_2$). (i) Work out an expression of the work done by the gas in this process. (ii) Show that the heat-capacity of the gas through the polytropic process is $C_m = \frac{m-\gamma}{m-1}C_v$, where $\gamma = C_p/C_v$, and $C_v$, $C_p$ are constant-volume and constant-pressure heat capacities, respectively, of the ideal gas.
