JEE Physics 2023 Question with Solution

Given: Hydrogen and Argon are in the same flask at temperature $30^\circ C$.

Find: The ratio $\frac{K_{argon}}{K_{hydrogen}}$.

The average kinetic energy per molecule of an ideal gas is

$$K = \frac{3}{2}kT$$

where $k$ is the Boltzmann constant and $T$ is the absolute temperature.

Since average kinetic energy per molecule depends only on temperature, it does not depend on the mass or nature of the gas.

Both gases are at the same temperature in the same flask, so

$$K_{argon} = \frac{3}{2}kT, \qquad K_{hydrogen} = \frac{3}{2}kT$$

Therefore,

$$\frac{K_{argon}}{K_{hydrogen}} = \frac{\frac{3}{2}kT}{\frac{3}{2}kT} = 1$$

Therefore, the ratio of average kinetic energies is $1$. The correct option is B.

Given: Both gases are in the same flask at the same temperature.

Find: The ratio of average kinetic energy per molecule.

Shortcut idea: For any ideal gas, average kinetic energy per molecule depends only on temperature. Therefore, if two gases have the same temperature, their average kinetic energies per molecule are equal.

So directly,

$$\frac{K_{argon}}{K_{hydrogen}} = 1$$

Hence, the correct option is B.