Question:
In a dilute gas at pressure $P$ and temperature $T$, the mean time between successive collisions of a molecule varies with $T$ is :
Correct Option: , 2
Solution:
(2) Mean free path, $\lambda=\frac{1}{\sqrt{2} \pi n d^{2}}$
where, $d=$ diameter of the molecule
$n=$ number of molecules per unit volume
But, mean time of collision, $\tau=\frac{\lambda}{v_{\mathrm{rms}}}$
But $v_{\mathrm{rms}}=\sqrt{\frac{3 k T}{R}}$
$\therefore \tau=\frac{\lambda}{\sqrt{\frac{3 k T}{m}}} \Rightarrow t \propto \frac{1}{\sqrt{T}}$
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