Q 11-12-123JEE MainJEE Main 2020 (6 Sep, Shift 2)Medium
In a dilute gas at pressure $P$ and temperature $T$, the time between successive collisions of a molecule varies with $T$ as:
Answer: (D) $\sqrt T$
Mean free path: $\lambda = \dfrac{k_BT}{\sqrt2\pi d^2P}$, so at fixed pressure $\lambda \propto T$.
Mean speed: $\bar v \propto \sqrt T$.
Mean time between collisions:
$$\tau = \frac{\lambda}{\bar v} \propto \frac{T}{\sqrt T} = \sqrt T$$
(The official answer key lists $\dfrac{1}{\sqrt T}$, which would hold at fixed volume, i.e. fixed number density, not at the stated fixed pressure.)
Solution by Sreeraj P, M.Sc Physics