JEE Main 2022 — Kinetic Theory of Gases Question with Solution

According to kinetic theory of gases,

A. The motion of the gas molecules freezes at $0 \mathrm{K}$.  

B. The mean free path decreases on increasing the number density of the molecules.

C. The mean free path increases on increasing the volume. Now if temperature is increased by keeping the pressure constant the volume should increase that is mean free path increases. 

Mean free path $\lambda =\frac{1}{\sqrt{2}\pi d^{2}n}$, here, $n=\frac{N}{V}$

$\Rightarrow \lambda =\frac{1}{\sqrt{2}\pi d^2{\displaystyle \frac{N}{V}}}$

Using, $PV=NKT$

$\Rightarrow \lambda =\frac{KT}{\sqrt{2}\pi d^{2}P}$ 

D. Average kinetic energy per molecule per degree of freedom is $\frac{1}{2}{k}_{B}T$.

Thus, B and C only.