Performance Optimization of the Carnot and Joule Cycles and Relationship with the Formulation of Physical Exergy Property

The present theoretical study proposes an analysis, underpinned by the basic foundations reported in the literature, aimed at establishing a generalization of the relationship between cyclic thermo-mechanical conversion processes and the physical exergy property defined for a system interacting with two different and independent reservoirs. The outcome of the study is the demonstration that physical exergy expresses both useful work or useful heat, if these interactions undergo conversion when withdrawn from a system. The approach to conversion consists in comparing the efficiency of (ideal) Carnot and Joule cycles leading to the argument that the Joule cycle is the one performing at maximum efficiency between two constant pressures, similarly to the Carnot cycle performing at maximum efficiency between two constant temperatures. In terms of specific (per cycle) work or heat of Carnot and Joule cycles, the study proves that the roles of temperature and pressure are opposed as evidenced by a performance optimization analysis for the two cycles. Interactions between a system and two independent reservoirs undergoing isothermal and isobaric processes respectively are examined in relation to useful work and useful heat. The aim and the novelty of this analysis is to explore the role of the Joule cycle and the pressure of system and isobaric reservoir, which are similar to the role of the Carnot cycle and the temperature of system and isothermal reservoir. This implies a generalized formulation of physical exergy which, for this reason, may be regarded as a temperature-and-pressure-dependent property in the general case of a system interacting with two reservoirs. Finally, the expression of the thermal and mechanical components of physical exergy, depending on temperature and pressure, and their relationship with the Carnot and Joule cycles, are envisaged as possible consequences of this analysis representing the basis for future research.