A Comparison of the Entropy of Thermal Radiation to that of Heat Conduction

Many thermodynamic texts imply that the entropy flux for thermal radiation (TR) is the same as that for heat conduction, the heat flux divided by the local temperature (q/T). However, for blackbody radiation (BR) emission a 4/3 coefficient occurs and recently it was shown that for non-blackbody radiation (NBR) the coefficient is greater than 4/3 [1]. Some of the fundamental equations that are used in thermodynamics express the entropy flux of heat transfer in a q/T type form. In this paper we address the use of the Clausius equality, and expressions extended from it for irreversible processes, when TR is involved. We find that the Clausius equality for reversible processes is applicable, while the statements extended for irreversible processes are not applicable. Also, we present an alternative derivation of the 4/3 coefficient that shows in a direct way that it follows from the observable relation between BR energy and emission temperature (i.e., energy is proportional to T⁴). This is done without defining radiation pressure or using Planck’s spectral entropy radiance expression.