Reversible and irreversible heat transfer by radiation

Abstract

The theme of heat transfer by radiation is absent from most textbooks on thermodynamics, and its treatment in the applied literature presents some basic discrepancies concerning the validity of the Clausius relation between the quantity of heat exchanged, , and the accompanying entropy change, dS. We review the reversible and irreversible heat transfers by radiation to clarify the validity of the Clausius relation, and we show that in both cases, the Clausius relation is obeyed, as it should be. We also deal with radiation diluted by the presence of matter, introducing a dilution coefficient, ϕ, and an irreversibility factor, . This treatment requires the use of the correct relation between energy and heat fluxes, the spectral fluxes of energy and entropy, and Planck’s equation for the entropy of monochromatic radiation. For the irreversible case of diluted radiation, we recover the ratio between the fluxes of heat and entropy that agree with Clausius’ inequality, including an irreversibility factor, . An improved modification for the explicit function is given. As an illustration, the fluxes of energy and entropy from the Sun to the Earth are obtained. We also calculate the fluxes re-emitted by the Earth, taking into account the greenhouse effect. We find the value of for the re-emitted entropy flux after the radiation has been thermalized, which is much larger than the incident flux, in agreement with other authors.