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A gas consists of N diatomic molecules. Two classical models are considered: Model I treats the diatomic molecule as a rigid dumbbell (two point masses connected by a rigid rod, 5 degrees of freedom), while Model II treats it as two point masses connected by a spring (allowing vibrational motion, 7 degrees of freedom). Which of the following statements about this gas is TRUE?

1. Model II has a smaller specific heat than Model I
2. Model I is always the correct description
3. Model II is always the correct description
4. The appropriate model depends on the temperature of the gas

Correct answer: The appropriate model depends on the temperature of the gas

Solution

According to the principle of equipartition and quantum considerations, vibrational degrees of freedom are only activated at sufficiently high temperatures. At low T, Model I (rigid rotor, 5 DOF) is appropriate; at high T, Model II (with vibration, 7 DOF) is appropriate. The choice depends on temperature.

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