A flask contains hydrogen and oxygen in the ratio of $2: 1$ by mass at temperature $27^{\circ} \mathrm{C}$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Heat & Thermodynamics

A flask contains hydrogen and oxygen in the ratio of

2 : 1

by mass at temperature

2 7^{\circ} C

. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

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

Answer: (B)

Solution

The average kinetic energy of a gas molecule is set only by the absolute temperature,

\overset{ˉ}{E} = \frac{f}{2} k T

, and does not depend on the molecular mass or on how much of each gas is present. Hydrogen and oxygen in the flask share the same temperature of

2 7^{\circ}

C, so each molecule of either gas carries the same average kinetic energy, and the required ratio is

1 : 1

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Single correct option

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