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 `(C_(P))/(C_(V))= gamma` for this gas, then a good estimate for `(tau_(2))/(tau_(1))` is given by

Options

A. `(1)/(2)`
B. 2
C. `((1)/(2))^(gamma)`
D. `((1)/(2))^((gamma)/(2) +1)`

Explanation

Relaxaation time `tau prop (V)/(sqrtT) and T prop (1)/(V^(gamma-1))`
`:. tau prop V^(1 + (gamma-1)/(2))`
`:. tau= V^((1 + gamma)/(2))`
`:. (tau_(1))/(tau_(i)) = ((2V)/(V))^((1 + gamma)/(2)) = (2)^((1 + gamma)/(2))`