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 \(\left( {\gamma = \frac{{{C_P}}}{{{C_V}}}} \right)\)

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Correct Answer

(B) \(\;\frac{{\gamma + 1}}{2}\)

Step-by-step Solution

Detailed explanation

\(\tau = \frac{1}{{\sqrt 2 \pi {d^2}\left( {\frac{N}{V}} \right)\sqrt {\frac{{3RT}}{M}} }}\)

\(\tau \propto \frac{V}{{\sqrt T }}\)

\(As,\,T{V^{\gamma - 1}} = K\)

\(So,\,\tau \propto {V^{\gamma + 1/2}}\)

\(Therefore,\,q = \frac{{\gamma + 1}}{2}\)

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