Polylogarithmic Representation of Radiative and Thermodynamic Properties of Thermal Radiation in a Given Spectral Range: I. Blackbody Radiation

Abstract

There are several classes of materials and space objects for which the frequency dependence of the spectral emissivity is represented as a power series. Therefore, the study of the properties of thermal radiation for these real bodies is an important task for both fundamental science and industrial applications. The general analytical expressions for the thermal radiative and thermodynamic functions of a real body are obtained in a finite range of frequencies at different temperatures. 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 obtained 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 and 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 the wavenumber domain.