In a dilute gas at pressure P and temperature | vedclass

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Question

(A) The mean free path $\lambda$ is given by $\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$,where $k_B$ is the Boltzmann constant and $d$ is the molecul

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$\sqrt{T}$

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(A) The mean free path $\lambda$ is given by $\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$,where $k_B$ is the Boltzmann constant and $d$ is the molecular diameter.For a constant pressure $P$,$\lambda \propto T$.The average speed of a molecule $v_{avg}$ is given by $v_{avg} = \sqrt{\frac{8 k_B T}{\pi m}}$,so $v_{avg} \propto \sqrt{T}$.The mean time between successive collisions $t_0$ is defined as $t_0 = \frac{\lambda}{v_{avg}}$.Substituting the proportionalities: $t_0 \propto \frac{T}{\sqrt{T}} = \sqrt{T}$.Therefore,the mean time between successive collisions varies with $T$ as $\sqrt{T}$.

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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