JEE Main 2025 Apr 2 Shift 1, Physics Q24: Law of Equipartition of Energy

JEE Main2025Apr 2, Shift 1Physics

$γ_{A}$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $γ_{B}$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{γ _{A}}{γ _{B}} = (1 + \frac{1}{n})$ , then the value of $n$ is ______.

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Solution

For a gas with $f$ degrees of freedom (with each vibrational mode counting as 2 in equipartition: 1 kinetic + 1 potential):

$γ = \frac{f + 2}{f}$

Gas A (monoatomic): $f_{A} = 3$ (translational only).

$γ_{A} = \frac{3 + 2}{3} = \frac{5}{3}$

Gas B (polyatomic): $f_{B} = 3 + 3 + 2 (1) = 8$ (1 vibrational mode contributes 2 degrees of freedom).

$γ_{B} = \frac{8 + 2}{8} = \frac{10}{8} = \frac{5}{4}$

Ratio:

$\frac{γ _{A}}{γ _{B}} = \frac{5/3}{5/4} = \frac{4}{3} = 1 + \frac{1}{3}$

Comparing with $1 + \frac{1}{n}$ gives $n = 3$ .

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JEE Main 2025 Apr 2 Shift 1, Physics Q24: Law of Equipartition of Energy

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