In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as :

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$T$

$\frac{1}{\sqrt{T}}$

$\frac{1}{T}$

$\sqrt{T}$

answer is A.

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Detailed Solution

Mean free path $λ = \frac{R T}{\sqrt{2} π d^{2} N_{A} P}$
So mean time between successive collisions is
$τ = \frac{λ}{v_{r m s}} = \frac{R T}{\sqrt{2} π d^{2} N_{A} P \sqrt{\frac{3 R T}{M}}}$

So $τ \propto \sqrt{T}$

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