JEE Main 2026 — Kinetic Theory of Gases Question with Solution

The average kinetic energy of a gas molecule is directly proportional to its absolute temperature and is given by $E=\frac{f}{2}{k}_{B}T$, where $f$ is the degree of freedom. Since both $H_2$ and $O_2$ are diatomic gases, they have the same degrees of freedom ($f=5$). Therefore, if their average kinetic energies are the same, their temperatures must be the same. Thus, Assertion A is true.

The root mean square (r.m.s.) speed of a gas molecule is given by $v_{rms}=\sqrt{\frac{3RT}{M}}$. Since the molar mass $M$ of $H_2$ ($2\text{ g/mol}$) is different from that of $O_2$ ($32\text{ g/mol}$), their r.m.s. speeds will be different even at the same temperature. Thus, Reason R is false.

Therefore, A is true but R is false.

Answer: A is true but R is false