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

Answer

C

Explanation

Since `tau = (1)/(npi sqrt(2)V_(rms)d^(2))`
`n prop (1)/(V)` and `V_(rms) prop sqrt(T)`
`rArr tau prop (V)/(sqrt(T))`
`n = C_(1)V^(-1) ltvgt = C_(2)T^(1//2)`
since `TV^(gamma-1) = constant rArr tau prop V^((gamma+1)/(2))`