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The mean free path of a gas is given by $λ = 1 / (\sqrt{2} π σ^{2} N^{})$ where $σ$ is the molecular diameter and N is the number of molecules per unit volume. It implies that

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$λ \propto p / T$

$λ$ is independent of T and p

$λ \propto T / p$

$λ \propto (p / T)^{2}$

answer is C.

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Detailed Solution

We have

$p V = n R T = \frac{N}{N_{A}} R T \Rightarrow N^{*} = \frac{N}{V} = \frac{p N_{A}}{R T} = \frac{p}{k T}$

Hence, $λ = \frac{k T}{\sqrt{2} π σ^{2} p}$

This gives $λ \propto T / p$

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