Thermal Physics - Equipartition Law

A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. The average total energy of oscillator is

A. ½kT
B. kT
C. ³⁄₂kT
D. 3kT
E. 6kT

(GR0177 #05)

Solution:

Equipartition of Energy: E = ½ fkT

f = Degree of Freedom (DoF)

3D harmonic oscillator has 6 DoF = 3 components of momentum (kinetic energy) and 3 components of position (potential energy)
→ E = ⁶⁄₂ kT = 3kT

Answer: D