  The general form of the Stefan-Boltzmann law for the energy density of
black-body radiation is generalized to a spacetime with extra dimensions using
standard kinetic and thermodynamic arguments. From statistical mechanics one
obtains an exact formula. In a field-theoretic derivation, the Maxwell field
must be quantized. The notion of electric and magnetic fields is different in
spacetimes with more than four dimensions. While the energy-momentum tensor for
the Maxwell field is traceless in four dimensions, it is not so when there are
extra dimensions. But it is shown that its thermal average is traceless and in
agreement with the thermodynamic results.
