**The Stefan Boltzmann Law of
Radiation**

*---- NOT COVERED IN SPRING 1999 OR SPRING 2000----*

From Physics 231 we know that systems at a
higher temperature are composed of particles with a higher kinetic energy. This is true
for thermalized photons as well. For a gas of non-relativistic particles, the average
energy per particle was ** (3/2)kT**. For photons the average energy
per photon will be

Since the average energy per photon is
proportional to the temperature, and the energy of a photon is inversely related to it's
wavelength, *E = hc/*** l**, one can see that the spectrum of light from a hot object is
related to it's temperature.

From the Heisenberg uncertainty principle we can
determine that the number of photon states with momentum less than ** p_{max}**
and within a three dimensional volume

,

where ** h** is Planck's constant.
Since the characteristic cutoff of the momentum

The Stefan-Boltzmann constant ** s**
was used in Physics 231, but here we see that it can be found in terms of fundamental
constants including Planck's constant. Historically, this was how Planck came upon the
constant.