Consider an ideal gas confined in an isolated closed chamber . As the gas undergoes an adiabatic expansion , the average time of collision between molecules increases as $V^{q}$, Where V is the volume of the gas . The value of q is : $\bigg(\gamma = \large\frac{C_p}{C_v}\bigg) $

Question

$\begin{array}{1 1} \frac{\gamma -1}{2} \\ \frac{3\gamma +5 }{6} \\ \frac{3 \gamma -5}{6} \\ \frac{\gamma +1}{2} \end{array} $