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Consider two identical diatomic gases A and B at same 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 m/4. The ratio of the specific heats (C_V^A and C_V^B) of gas A and B, respectively, is-

1. 5: 9
2. 7: 9
3. 3: 5
4. 5: 7

Correct answer: 5: 7

Solution

Gas A (rigid diatomic) has Cv=5/2 R. Gas B (diatomic + one vibrational mode) has Cv=5/2 R + R = 7/2 R. The ratio Cv_A:Cv_B = (5/2):(7/2) = 5:7.

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