an extended formulation of physical exergy

the mechanical aspect of entropy-exergy relationship, together with the thermal aspect usually consid-ered, leads to an extended formulation of physical exergy based on both maximum useful work and maximum useful heat that are the outcome of available energy of a thermodynamic system. this approach suggests that a mechanical entropy can be studied, in addition to the already used thermal entropy, with respect to work interaction due to volume variation. the mechanical entropy is related to energy transfer by means of work and it is complementary to the thermal entropy that accounts energy transfer by means of heat. furthermore, the paper proposes a definition of exergy based on carnot cycle that is reconsidered in the case the inverse cycle is adopted and, as a consequence, the concept that work depends on pressure similarly as heat depends on temperature, is pointed out. then, the logical sequence to get mechanical exergy expression to evaluate work withdrawn from available energy is demonstrated. on the basis of the mechanical exergy, the mechanical entropy set forth is deduced in a general form valid for any process. finally, the extended formulation of physical exergy is proposed, that summarizes the contribution of ei-ther heat and work interactions and related thermal exergy as well as mechanical exergy that both result as the outcome from the available energy of the system interacting with an external reference environ-ment (reservoir). the extended formulation contains an additional term that takes into account the vol-ume, and consequently the pressure, that allows to evaluate exergy with respect to the reservoir character-ized by constant pressure other than constant temperature. the conclusion is that the extended physical exergy takes into account the equality of pressure, other than equality of temperature, as a further condi-tion of mutual stable equilibrium state between system and reservoir.