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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?

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  • $\begingroup$ 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. $\endgroup$
    – Qmechanic
    Oct 31, 2023 at 16:51

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It's an analogy. Each cavity mode behaves like a mechanical harmonic oscillator. For example, you can excite a mode by a probe inserted into the cavity, and the excitation versus frequency will have the Lorentzian shape associated with a harmonic oscillator. So, given that a mode behaves that way, it is natural to attempt to construct the statistical mechanics of radiation using the Rayleigh-Jeans approach. And it matches experiments at low frequency, so it would seem to be on the right track. But high frequency requires a more sophisticated theory.

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