question_answer

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as \[{{V}^{q}},\] where V is the volume of the gas. The value of q is : \[\left( \gamma =\frac{{{C}_{p}}}{{{C}_{v}}} \right)\]                                      [JEE MAIN 2015]

A)  \[\frac{\gamma +1}{2}\]

B)       \[\frac{\gamma -1}{2}\]

C)  \[\frac{3\gamma +5}{6}\]        

D)       \[\frac{3\gamma -5}{6}\]

Correct Answer: A

Solution :

           

[a] Average time of collisim between molecules is

mean free path

So

andconstant

So