Statistical thermodynamics approach for the available work transported by particle fluxes

Abstract

The theory covers cases when the exergy concept is not fully relevant. An indicator called work content factor is used to quantify the proportion of available work in a given amount of energy. General expressions have been obtained for the flux of available work transported by particles, the rate of work deficiency and the work content factor. More specific results have been obtained for the work content factor of the low-speed and ultra-relativistic particle fluxes, respectively, by using several assumptions concerning the number of energy states, the mean occupation number of the energy states, the entropy and the module and direction of the particles speed. The theory includes extraction of work from particle fluxes governed by classical kinetic theory and heat as particular cases and has been applied to fluxes of fermions (electrons) and bosons (Helium-4) in both the low-speed and ultra-relativistic case. It has been shown that the emission of thermal photons is several orders of magnitude lower than the stimulated particle emission by the primary work extractor. As a result, a unique expression of the work content factor of the ultra-relativistic particle fluxes has been obtained for both fermions and bosons while another expression has been derived for low-speed fermions and bosons. Generally, the work content factor decreases by increasing the temperature Tc of the primary work extractor. In some cases, at large values of Tc and small values of the average directional factor of the source of particle, work cannot be extracted from the energy of the particle flux.