Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecules changes from $$\tau_1$$ to $$\tau_2$$. If $$\frac{C_p}{C_v} = \gamma$$ for this gas then a good estimate for $$\frac{\tau_2}{\tau_1}$$ is given by

A

2

B

$$\frac{1}{2}$$

C

$$\left(\frac{1}{2}\right)^\gamma$$

D

$$\left(\frac{1}{2}\right)^{\frac{\gamma+1}{2}}$$