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COMEDK202510 May 2025Morning ShiftPhysicsKinetic Theory of GasesActual

The mean energy per molecule for a diatomic gas is:

Options

  1. A( 3 2 N ) K _ B T
  2. B( 3 2 ) K _ B T
  3. C( 5 2 N ) K _ B T
  4. D( 5 2 ) K _ B T

Correct answer

D. ( 5 2 ) K _ B T

Step-by-step solution

A diatomic gas molecule at moderate temperatures possesses 5 degrees of freedom: 3 translational and 2 rotational degrees of freedom. According to the law of equipartition of energy, each degree of freedom contributes 1 2 K_ B T to the average energy of the molecule. The total mean energy per molecule E is given by the sum of the energies associated with each degree of freedom: E = f ( 1 2 K_ B T ) Substituting f = 5 for a diatomic gas: E = 5 ( 1 2 K_ B T ) = 5 2 K_ B T Answer: ( 5 2 ) K _ B T

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