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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 : $(γ = \frac{C_{P}}{C_{V}})$

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$\frac{3 γ + 5}{6}$

$\frac{γ - 1}{2}$

$\frac{3 γ - 5}{6}$

$\frac{γ + 1}{2}$

answer is A.

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Detailed Solution

$τ = \frac{1}{\sqrt{2} {πd}^{2} (\frac{N}{V}) \sqrt{\frac{3 RT}{M}}} τ \propto \frac{V}{\sqrt{T}} As, {TV}^{γ - 1} = constant So, τ \propto V^{\frac{γ + 1}{2}} Therefore, q = \frac{γ + 1}{2}$

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