On the radiative and thermodynamic properties of the Cosmic Microwave   Background radiation using COBE FIRAS instrument data
  Use formulas to describe the monopole and dipole spectra of the Cosmic Microwave Background (CMB) radiation, the exact expressions for the temperature dependences of the radiative and thermodynamic functions, such as the total radiation power per unit area, total energy density, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume, pressure, enthalpy density, and internal energy density in the finite range of frequencies are obtained. Since the dependence of temperature upon the redshift z is known, the obtained expressions can be simply presented in z representation. Utilizing experimental data for the monopole and dipole spectra measured by the COBE FIRAS instrument in the 60 - 600 GHz frequency interval at the temperature T = 2.728 K, the values of the radiative and thermodynamic functions, as well as the radiation density constant a and the Stefan-Boltzmann constant are calculated. In the case of the dipole spectrum, the constants a and the Stefan-Boltzmann constant, and the radiative and thermodynamic properties of the CMB radiation are obtained using the mean amplitude Tamp = 3.369 m K. It is shown that the Doppler shift leads to a renormalization of the radiation density constant a, the Stefan-Boltzmann constant, and the corresponding constants for the thermodynamic functions. The radiative and thermodynamic properties of the Cosmic Microwave Background radiation for the monopole and dipole spectra at the redshift z = 1089 are calculated. 
Anatoliy I. Fisenko, Vladimir Lemberg
astro-ph.CO