Physics Q33 – JEE-MAIN 2025

Home Physics ThermodynamicsQuestion #534

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is : \ (Give : Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

Clue 1 of 3: Kinetic Theory of Gases

The average kinetic energy of gas molecules is directly related to the absolute temperature of the gas.

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Ninja Strategy•Fundamental Principle Recall

Recall that the average kinetic energy per molecule depends only on temperature, not on the type or molar mass of the gas.

🧠 Full Solution Path

Step 1: Identify the governing principle✦ Active

According to the Kinetic Theory of Gases, the average translational kinetic energy per molecule of an ideal gas is solely dependent on its absolute temperature. It is independent of the type of gas, its molar mass, or its atomic structure.

Step 2: State the formula for average kinetic energy○ Expand

The average kinetic energy per molecule ( $E_{a v g}$ ) is given by the formula:

E_{a v g} = \frac{3}{2} k T

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

Step 3: Calculate the ratio○ Expand

Given that both helium (He) and argon (Ar) are at the same room temperature ( $T = 300 K$ ), their average kinetic energies per molecule will be identical.

\frac{E_{a v g, H e}}{E_{a v g, A r}} = \frac{\frac{3}{2} k T}{\frac{3}{2} k T} = 1

Therefore, the ratio of average kinetic energies of helium to argon is $1 : 1$ .

💡 Teacher's Secret Hint

The molar masses provided are distractors; they are not needed for calculating the average kinetic energy per molecule.

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Physics Question 33 – JEE-MAIN 2025

Clue 1 of 3: Kinetic Theory of Gases

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