JEE Physics 2024 Question with Solution

Given: The question asks which parameter remains the same for molecules of all gases at a given temperature.

Find: The correct option.

From kinetic theory, the average kinetic energy of a gas molecule depends only on absolute temperature: $E_k = \frac{3}{2}kT$ Here, $k$ is the Boltzmann constant and $T$ is the absolute temperature.

Therefore, at the same temperature, molecules of all gases have the same average kinetic energy.

• Momentum depends on mass and speed, so it varies from gas to gas.
• Mass depends on the type of gas, so it is not the same.
• Speed also varies because different gases have different molecular masses.

Therefore, the correct option is A.

The solution explicitly concludes that the parameter common to all gases at a given temperature is kinetic energy.

Given: Same temperature for different gases.

Find: Which molecular parameter is unchanged.

Use the direct result of kinetic theory and equipartition: temperature measures the average kinetic energy of molecules. So if temperature is fixed, average kinetic energy is fixed.

Thus, the correct option is A.