Activity: Applying the equipartition theorem

Contemporary Challenges 2021 (5 years)
Students count the quadratic degrees of freedom of a few toy molecules to predict their internal energy at temperature \(T\).
  • Media
    • activity_media/four-rods.png
    • activity_media/one-rod.png
    • activity_media/one-spring.png
    • activity_media/three-springs.png
This follows Equipartition theorem
If the microscopic world was classical, predict \(U_{\text{classical}}(T)\) for the following “toy molecules” in the gas phase.
(a) (b) (c) (d)
  • Each ball is a point mass \(m\) with no moment of inertia.
  • The zig-zag lines are springs which are freely jointed at the balls.
  • Vibrational motion of the springs is very small (\(\ll\) the length of the spring).
  • The springs can extend and compress, but cannot twist or flex.
  • The straight lines are rigid rods.
Keywords
equipartition theorem
Learning Outcomes