If $T_2$ and $T_2^{\mathrm{\prime }}$ are the respective temperatures of a gas undergoing adiabatic reversible and irreversible expansions from the volume $V_1$ to $V_2$ , which of the following facts holds good:

where  $\gamma$ is the ratio $C_{p,\mathrm{m}}/C_{V,\mathrm{m}}$ of the gas.