A flask contains argon and oxygen in the ratio of 3:2 in mass and the mixture is kept at $27^{\circ} \mathrm{C}$. The ratio of their average kinetic energy per molecule respectively will be :

JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Heat & Thermodynamics

A flask contains argon and oxygen in the ratio of 3:2 in mass and the mixture is kept at

2 7^{\circ} C

. The ratio of their average kinetic energy per molecule respectively will be :

(A) $3 : 2$
(B) $9 : 4$
(C) $2 : 3$
(D) $1 : 1$ ✓ Correct

Answer: (D)

Solution

The mean translational kinetic energy of a single molecule of an ideal gas is

\frac{3}{2} k_{B} T

, a quantity fixed by the absolute temperature alone. Both argon and oxygen share the one flask at

2 7^{\circ} C = 300 K

, so every molecule of either gas carries the same average kinetic energy irrespective of its mass or chemical identity; the

3 : 2

mass proportion fixes how many molecules of each are present but not the energy per molecule. The ratio of average kinetic energy per molecule is therefore

1 : 1

JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Heat & Thermodynamics

Solution

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