The Clausius inequality corrected for heat transfer involving radiation

Abstract

The objective of this paper is to prove that the Clausius inequality must be re-stated to have general applicability for heat transfer involving radiative fluxes. The integrand (đ Q/ T) of the Clausius expression applies to heat conduction and convection, but does not hold for most radiative transfer scenarios, with the exception of reversible infinitesimal net blackbody radiation transfer. In other cases involving radiative transfer, the equality holds for a cycle even though irreversible heat addition by radiative transfer occurs. This is without the erroneous presumption of entropy destruction anywhere in the cycle. Thus, the Clausius inequality indicates reversibility for a cycle that includes an irreversible process. Further, in some radiative cases the quantity đ Q/ T, where T is the boundary temperature, is not the entropy transfer at the system boundary, and in fact, primarily represents entropy production within the system. It is also clear that in another case considered, the quantity đ Q/ T had no physical meaning whatsoever. Consequently, the Clausius expression has been re-stated so that it is applicable to cycles with processes involving any form of heat transfer. A new integrand (đ Q cc/ T + đ S Net,Rad) is presented, allowing the Clausius inequality to generally apply to all heat transfer scenarios. The work in this paper emphasizes the need to re-state other fundamental equations allowing applicability to all heat transfer processes, and draws attention to the unique character of radiative entropy calculations.