Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increase as `V^q`, where V is the volume of the gas. The value of q is : `(gamma=(C_p)/(C_v))`

Options

A. `(gamma +1)/(2)`
B. `(gamma -1)/(2)`
C. `(3gamma +5)/(6)`
D. `(3gamma -5)/(6)`

Answer

A

Explanation

`tau alpha ("Volume")/(v_("avg"))`
`tau alpha V^(1)T^(-1)/(2)`
For adiabatic process
`T alphaV^(1-gamma)`
`tau alpha V^(1)T^(-1//2) alpha V^(gamma+1)/(2)` comparing `q = (gamma+1)/(2)`