This lecture introduces the equipartition theorem.

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.

Students sketch the temperature-dependent heat capacity of molecular nitrogen. They apply the equipartition theorem and compute the temperatures at which degrees of freedom “freeze out.”