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

TL;DR

This paper derives analytical formulas for the radiative and thermodynamic properties of real-body thermal radiation within a spectral range, using polylogarithm functions, and applies them to zirconium carbide at melting point.

Contribution

It introduces general analytical expressions for thermal properties of real bodies with frequency-dependent emissivity, extending previous models and applying them to zirconium carbide.

Findings

Identified differences in radiative properties between liquid and solid zirconium carbide.

Validated analytical formulas with experimental emissivity data.

Observed gaps between properties of liquid and solid states.

Abstract

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.