Absorbing Blackbody Radiation
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A perfect blackbody is one that absorbs all the radiation, light that falls on it. Since there is energy in radiation there is a certain energy density in the cavity, u = U/V, where U is the energy, V is the volume and u is the energy density. From electromagnetic theory, the pressure exerted by the radiation is p=1/3u, and experiment shows that the energy density is independent of volume, u=u(T). the relation between u and T is obtained from the thermodynamic equation of state:
(∂U/∂V)T = T(∂P/∂T)V - P
After substitution, manipulation and integration of the equations show that u = α T4 , where α is a constant
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