The big-bang theory of the universe makes the following thermodynamic assertion: the radiation energy initially confined in a small region undergoes a spherically symmetric expansion. Show explicitly from thermodynamics considerations that in adiabatic expansion the radiation cools, that is, show that R x 1/T, where R is the radius of the spherical region and T' is the associated temperature. Assume that the radiation pressure P = u/3, where the energy density u (defined as the ratio of internal energy U to the volume V) is given by u = eT4, e being a constant.