# How is the average energy, $k_BT$, associated with each mode of electromagnetic radiation confined in a cavity described in Rayleigh-Jeans Law?

From Rayleigh-Jeans law we can get an expression for the energy density of black-body radiations confined in a cavity.

When blackbody radiations i.e. electromagnetic waves are confined into a cavity than according to classical electronmagnetic theory radiations will form standing waves.

In the book to calculate the total energy density of the blackbody radiations inside the cavity, first they have calculated the number of modes i.e. number of standing wave patterns of electromagnetic radiations. After that it was said that average energy associated with each mode is $$k_BT$$.

Please explain how we can conclude that average energy associated with each mode is $$k_BT$$.

On this link it is said that

"The average kinetic energy per degree of freedom is $$\frac{1}{2}kT$$. For harmonic oscillators there is an equality between kinetic and potential energy so the average energy per degree of freedom is $$kT$$."

Please explain how does the harmonic oscillator comes into the picture in all this discussion?

• Minor comment to the post (v2): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. Oct 31, 2023 at 16:51