JEE Main 2025 Jan 28 Shift 2, Physics Q4: Kinetic Theory of an Ideal Gases

JEE Main2025Jan 28, Shift 2Physics

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
$\frac{5}{2}$
D
$\frac{4}{25}$

Solution

At a fixed temperature, $v_{r m s} = \frac{3 R T}{M}$ , so $v_{r m s} \propto \frac{1}{M}$ . Vapour density is proportional to molar mass, hence $v_{r m s} \propto \frac{1}{ρ}$ .

$\frac{( v _{r m s} ) _{1}}{( v _{r m s} ) _{2}} = \frac{ρ _{2}}{ρ _{1}} = \frac{25}{4} = \frac{5}{2}$ .

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JEE Main 2025 Jan 28 Shift 2, Physics Q4: Kinetic Theory of an Ideal Gases

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