Mean Free Path & Real Gases question from MHT CET 2024 (2 May, Shift 1)

Answer: (b)

1. $\lambda = \dfrac{1}{\sqrt{2}\,n\pi d^2}$ depends only on number density $n$ and $d$.
2. At constant volume (fixed amount of gas) $n$ does not change when $T$ changes.
3. So $\lambda$ stays $1500\,d$, i.e. option (a).
4. Option (b) $\dfrac{373}{273}\times1500\,d$ would be correct only at constant pressure, where $\lambda = \dfrac{kT}{\sqrt{2}\pi d^2 P} \propto T$.