Question

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 m/4. The ratio of the specific heats (C^A_V and C^B_V ) of gas A and B, respectively is :

(1) 7 : 9

(2) 5 : 7

(3) 3 : 5

(4) 5 : 9

Answer 1

Answer is (2) 5 : 7

Molar heat capacity of A at constant volume = 5R/2 

Molar heat capacity of B at constant volume = 7R/2

Dividing both, (C_V)_A/(C_V)_B = 5/7

Answer 2

Answer is (2) 5 : 7

Degree of freedom of a diatomic molecule if vibration is absent = 5

Degree of freedom of a diatomic molecule if vibration is present = 7