The mean free path of molecules of an ideal gas at absolute temperature $T$ and pressure $P$ is inve

Question

The mean free path of molecules of an ideal gas at absolute temperature $T$ and pressure $P$ is inversely proportional to

Professor PC Thomas Classes · Answer

(a) : The mean free path is given by $\lambda = \frac{1}{\sqrt{2} n \pi d^2}$, where $n$ is the number density (number of molecules per unit volume). From the ideal gas equation $P = n k_B T$, we have $n = \frac{P}{k_B T}$. Substituting this into the mean free path formula gives $\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$. This shows that the mean free path is inversely proportional to the pressure $P$.