The specific heats, CP and CV of a gas of diatomic molecules, A, are given (in units of J mol–1 K–1) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :

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Physics

Degree of Freedom Internal Energy of Gas and Specific Heat Capacity of Gases

Question

The specific heats, C_P and C_V of a gas of diatomic molecules, A, are given (in units of J mol^–1 K^–1) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :

A has one vibrational mode and B has two

Both A and B have a vibrational mode each

A is rigid but B has a vibrational mode

A has a vibrational mode but B has none

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For A:

$\frac{C_{p}}{C_{v}} = γ = 1 + \frac{2}{f} = \frac{29}{22}$

It gives f = 6.3 ≈ 6 (3 translational, 2 rotational and 1 vibrational)

For B:

$\frac{C_{p}}{C_{v}} = γ = 1 + \frac{2}{f} = \frac{30}{21}$

⇒ f = 4.67

⇒ ≈ 5 (3 translational, 2 rotational, no vibrational)