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JEE Main 2020 (9 Jan, Shift 1) · Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation

Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation question from JEE Main 2020 (9 Jan, Shift 1)

Q46JEE Main 2020 · 9 JAN · SHIFT 1Medium

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

Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass $\frac{m}{4}$ . The ratio of the specific heats ( $C_V^A$ and $C_V^B$ ) of gas A and B, respectively is:

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Answer: (b)

Molar $C_V$ depends only on degrees of freedom, not on molecular mass.
Gas A (rigid diatomic): $C_V^A = \dfrac{5}{2}R$ .
Gas B (one vibrational mode): $C_V^B = \dfrac{5}{2}R + R = \dfrac{7}{2}R$ .
So the answer is (b) $5 : 7$ .

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