My quantum course starts with the Rayleigh-Jeans law derivation. Whilst I understand most of this, I'm not sure why the average energy of each mode is equal to what they say it is. For instance here is one explanation from hyperphysics: Assigning energy to the electromagnetic standing waves in a cavity draws on the principle of equipartition of energy. Each standing wave mode will have average energy kT where k is Boltzmann's constant and T the temperature in Kelvins. Why must each node have the same average energy? I understand why the number of nodes varies with wavelength and volume, just not why each has the same constant average energy. For instance my textbook says use the average energy from a Boltzmann distribution, which is kT, however why can you do so? I don't see the connection. I get what a Boltzmann distribution is, however why does each particle emit each node to an equal energy, as I seem to think using kT implies.