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Consider two ideal diatomic gases A and B at some temperature T. Molecules of gas A are rigid and have a mass m. Molecules of 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

Asked in JEE Main 9th Jan 1st Shift 2020 · Vibrational modes

Answer: (4) 5 : 7

Step-by-step solution

C_V=f/2R depends on the mode count, not on the molecular mass, so the masses are a distraction.

Gas A is a rigid diatomic: f=3+2=5, so C_V(A)=5/2 R.

Gas B has an additional vibrational mode, which counts twice: f=7, so C_V(B)=7/2 R.

(C_V(A))/(C_V(B))=5/7.

Why the other options are wrong

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