UY1: Crisis for equipartition theorem



Historical note: Crisis for the equipartition theorem at the end of the 1800s.

The prediction of the equipartition theorem does not agree with the measured heat capacity of gases.

  • Boltzmann: Defended the derivation of his equipartition theorem as correct, but suggested that gases might not be in thermal equilibrium.
  • Lord Kelvin: Suggested that the derivation for the equipartition theorem must be incorrect, since it disagreed with experiment, but was unable to show how.
  • Lord Rayleigh: Suggested that both the equipartition theorem and the experimental assumption of thermal equilibrium were both correct; to reconcile them, he noted that a “new principle” must be found to “escape from the destructive simplicity” of the equipartition theorem.
  • Einstein finally provided that escape in 1907 by showing that the anomaly was due to quantum effects: At low temperatures, some modes become “frozen” and no longer available to absorb energy.

Temperature dependence of Cv

Temperature dependence of Cv

– Rotational motion and then vibrational motion gets activated at increasing temperature.

Hence, at rotational mode, as temperature increase, the molecule do not vibrate harder. There is no energy used to increase the vibrational energy of the molecules. Hence, the vibrational mode do not contribute to the heat capacity at low temperature.

Next: Heat Capacity Of Solids

Previous: Heat Capacity Of Gases

Back To Thermodynamics


Back To Thermodynamics (University Year 1 Physics)

Back To University Year 1 Physics Notes



Mini Physics

As the Administrator of Mini Physics, I possess a BSc. (Hons) in Physics. I am committed to ensuring the accuracy and quality of the content on this site. If you encounter any inaccuracies or have suggestions for enhancements, I encourage you to contact us. Your support and feedback are invaluable to us. If you appreciate the resources available on this site, kindly consider recommending Mini Physics to your friends. Together, we can foster a community passionate about Physics and continuous learning.



Leave a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.