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

Polylogarithmic representation of radiative and thermodynamic properties of thermal radiation in a given spectral range: II. Real-body radiation