Exact and approximate statistical approaches for the exergy of blackbody radiation

There is a long term debate in literature about the exergy of blackbody radiation (BBR). Most authors contributing to this dispute used classical thermodynamics arguments. The objective of this paper is to propose a statistical thermodynamics approach. This gives new perspectives to previous results. Four simple statistical microscopic models are used to derive BBR exergy. They consist of combinations of quantum and classical descriptions of the state occupation number and entropy, respectively. In all four cases the BBR exergy (or exergy flux density) is given by the internal energy (or energy flux density) times an efficiency-like factor containing the environment temperature and the blackbody radiation temperature. One shows that Petela-Landsberg-Press efficiency is the "exact" result while the Jeter (Carnot) efficiency corresponds to the classical approximation. Other two (new) approximate efficiency-like factors are also reported.