For a diatomic gas, if γ₁ = ((Cp)/(Cv)) for rigid molecules and γ₂ =… | JEE Main 2025 (22 Jan, Shift 2)

Q11JEE Main 2025 · 22 JAN · SHIFT 2Medium

Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation

For a diatomic gas, if $\gamma_1 = \left(\frac{C_p}{C_v}\right)$ for rigid molecules and $\gamma_2 = \left(\frac{C_p}{C_v}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (Cp and Cv are specific heats of the gas at constant pressure and volume)

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Answer: (a)

$\gamma = 1 + \dfrac{R}{C_V}$ .
Vibrational modes increase $C_V$ , so $\gamma$ decreases.
Rigid: $\gamma_1 = 1.4$ ; with vibration, e.g. $\gamma_2 = \dfrac{9}{7} \approx 1.29$ .
So the answer is (a) $\gamma_2 < \gamma_1$ .

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Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation question from JEE Main 2025 (22 Jan, Shift 2)

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