# I Derive energy density proportional to emitted power per unit area

1. Jun 24, 2016

### Happiness

The following derives the relation that for a blackbody radiation the energy density is proportional to the energy emitted per unit area over unit time.

The average energy density $d\psi$ is obtained by dividing the radiant energy $dE$ received by the surface $dB$ in 1 second by the cylindrical volume $dV$ occupied by the radiation in 1 second.

I don't understand why $d\psi$ is uniform anywhere inside the cylinder, in particular, at points near the surface $dS$. At a point far away from $dS$, the point is always the same distance $\rho$ away from every part of $dS$. But this is not true for a point near $dS$. The point would be closer to some parts of $dS$. Then the energy density $d\psi$ at the point should not be uniform but vary depending on how far the point is from the center of the surface $dS$.

2. Jun 29, 2016