Law of Equipartition of Energy (Energy per DOF = ½kBT per molecule = ½RT per mole)
jee-mainjee-advanced
Energy per DOF = ½kBT per molecule = ½RT per mole
What each symbol means
| Symbol | What it stands for |
|---|---|
| R | Universal gas constant = 8.314 J mol⁻¹ K⁻¹ |
| T | Absolute temperature (K) |
| f | Number of degrees of freedom (3 mono, 5 diatomic rigid, 7 diatomic vib) |
| kB | Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹ |
| ε | Average energy per degree of freedom (J per molecule or J/mol) |
When to use this
Valid in classical limit (kBT >> quantum energy spacing). Each QUADRATIC term in the energy expression gets ½kBT. Translational and rotational DOF each contribute ½kBT. Vibration has 2 quadratic terms (KE + PE) per mode → contributes kBT per vibrational mode. Total energy per molecule = (f/2)kBT.