Heat and Thermodynamics

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from $${\tau _1}$$ to $${\tau _2}$$ . If $${{{C_p}} \over {{C_v}}} = \gamma$$ for this gas then a good estimate for $${{{\tau _2}} \over {{\tau _1}}}$$ is given by :