  The general analytical expressions for the thermal radiative and
thermodynamic properties of a real-body are obtained in a finite range of
frequencies at different temperatures. The frequency dependence of the spectral
emissivity is represented as a power series. The Stefan-Boltzmann law, total
energy density, number density of photons, Helmholtz free energy density,
internal energy density, enthalpy density, entropy density, heat capacity at
constant volume, pressure, and total emissivity are expressed in terms of the
polylogarithm functions. The general expressions for the thermal radiative and
thermodynamic functions are applied for the study of thermal radiation of
liquid and solid zirconium carbide. These functions are calculated using
experimental data for the frequency dependence of the normal spectral
emissivity in the visible-near infrared range at the melting (freezing) point.
The gaps between the thermal radiative and thermodynamic functions of liquid
and solid zirconium carbide are observed. The general analytical expressions
obtained can easily be presented in wavenumber domain.
