If the pressure of the gas is kept constant, then the mean free...

The mean free path of a gas molecule is given by

$\lambda = \dfrac{1}{\sqrt{2}\pi d^2 n}$

where $d$ is the diameter of the molecule and $n$ is the number of molecules per unit volume.

From the ideal gas equation, $P = n k_B T$, which gives $n = \dfrac{P}{k_B T}$.

Substituting this into the expression for mean free path, we get

$\lambda = \dfrac{k_B T}{\sqrt{2}\pi d^2 P}$

For a given gas at constant pressure, $P$ is constant. Therefore,

$\lambda \propto T$

Answer: $\lambda \propto T$