Planck's radiation law
From Glossary of Meteorology
Planck's radiation law
The distribution law of photon energies for radiation in equilibrium with matter at absolute temperature T: where E is photon energy, c is the free-space speed of light, h is Planck's constant, and k is Boltzmann's constant.
The integral of this function between any two energies is the contribution to the total irradiance from all photons with energies in this range. This law is mathematically similar and physically analogous to the Maxwell–Boltzmann distribution for the kinetic energies of (ideal) gas molecules in equilibrium. One of the salient differences between these two distributions is that the number of gas molecules within a container is conserved whereas the number of photons is not, increasing with the absolute temperature of the container. Within an enclosure the walls of which are opaque (but not necessarily black) and at temperature T, the distribution of photon energies is given by Planck's radiation law.
