Adiabatic change of state of photon gas

Summary form only given as follows. We previously introduced and justified the k problem as a thermodynamical contradiction of photon gas. In the thermodynamics of a photon gas the main contradiction is called the k problem; the piezotropic autobarotropic equation of state P=u/3 is adiabatic if k=1 exclusively, while the adiabatic connection PV/sup 4/3/=const (or rather the Poisson equation P/sub /spl thetav///sup -4/3/=const, /spl thetav/=u/c/sup 2/) requires that k=4/3. The present paper shows that the equations of state PV/sup 4/3/=const, TV/sup 1/3/=const, T/sup -4/3/P/sup 1/3/=const and P=u/3 cannot be valid for the adiabatic change of state of photon gas, simultaneously. Furthermore, Planck's distribution-and so the Wien's law and the Rayleigh-Jeans connection as well-cannot be invariant in case of adiabatic change of state of photon gas. Namely, in case of adiabatic change of state of photon gas, a new type of ultra-violet catastrophe appears. These results are of fundamental importance in the case of arbitrary deformation of electromagnetic radiation fields or quantum plasmas.