JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Heat & Thermodynamics

The ratio of vapour densities of two gases at the same temperature is

\frac{4}{25}

, then the ratio of r.m.s. velocities will be :

(A) $\frac{25}{4}$
(B) $\frac{2}{5}$
(C) $\frac{5}{2}$ ✓ Correct
(D) $\frac{4}{25}$

Answer: (C)

Solution

The r.m.s. speed of gas molecules is

v_{r m s} = \frac{3 R T}{M}

Since vapour density

ρ

is proportional to molar mass

M

at fixed conditions,

v_{r m s} \propto 1/ ρ

.

Given

\frac{ρ _{1}}{ρ _{2}} = \frac{4}{25}

the ratio of r.m.s. speeds is

\frac{v _{1}}{v _{2}} = \frac{ρ _{2}}{ρ _{1}} = \frac{25}{4} = \frac{5}{2}

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Single correct option

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