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The specific heats Cₚ 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:
- Both A and B have vibrational mode each.
- A is rigid but B has a vibrational mode.
- A has a vibrational mode but B has none.
- A has one vibrational mode and B has two.
Correct answer: A has a vibrational mode but B has none.
Solution
Cv = (f/2)R. Gas A has Cv = 22 -> f ~ 5.3, above the rigid-diatomic value 5, so A has a vibrational mode. Gas B has Cv = 21 ~ 5R/2 = 20.8 -> f ~ 5, so B is rigid with no vibrational mode. Hence A has a vibrational mode but B has none.
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