Since a black object at temperature T will emit as much radiation per unit time and frequency as it would absorb when placed inside a photon gas of temperature T, this means that a sphere will emit thermal radiation per unit frequency and unit area of c u ( nu ) dnu / 4.
22.
If I remember correctly, the entropy density of a photon gas is 4 / 3 u / T where u is the energy density, which in turn can be related to the Stefan-Boltzmann law via sigma T ^ 4 = c / 4 u . talk ) 22 : 04, 21 April 2010 ( UTC)
23.
:It might help to know that the energy density associated with a photon gas is \ sigma T ^ 4 \ over c ( someone check my proportionality constant ? ), which means that, for instance, the cosmic background radiation has an energy density of 1.04 \ times10 ^ {-14 } \ mathrm { J / m ^ 3 }, or a density of 1.16 \ times10 ^ {-31 } \ mathrm { kg / m ^ 3 }.
