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

Abstract

Using polylogarithm functions the exact analytical expressions for the radiative and thermodynamic properties of blackbody radiation, such as the Wien displacement law, 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, and pressure in the finite range of frequencies are constructed. The obtained expressions allow us to tabulate these functions in various finite frequency bands at different temperatures for practical applications. As an example, the radiative and thermodynamic functions using experimental data for the monopole spectrum of the Cosmic Microwave Background (CMB) radiation measured by the COBE FIRAS instrument in the 60 -600 GHz frequency interval at the temperature T = 2.725 K are calculated. The expressions obtained for the radiative and thermodynamic functions can be easily presented in wavelength and wavenumber domains.

Optimal frequency band interval to increase optical temporal coherence of thermal light

“…As it was shown in [27, see the chapters 5.1, 5.2], using the polylogarithmic representation for the function 11 ( , , ) p E v v T  [28,29], the conditions (2.5) can be presented in the form:…”

“…This optimization task was solved in [27]. The interval [v1, v1+∆] with a maximal value of the total energy density Ep (v, T) can be found from the following conditions: , ) [28,29], the conditions (2.5) can be presented in the form:…”

Polylogarithmic Representation of Radiative and Thermodynamic Properties of Thermal Radiation in a Given Spectral Range: II. Real-Body Radiation

“…In [39], it was pointed out that there are several classes of materials and space objects, for which the thermal radiative and thermodynamic properties within a finite spectral range of frequencies can be described using the polylogarithms functions. This means that the frequency dependence of   T ,   must be represented as a polynomial, for example.…”