Relative Free Energy Function and Structural Theory of Thermoeconomics

This paper explores the advantages of using relative free energy instead of exergy to build a mathematical theory of thermodynamic costs to diagnose malfunctions in thermal systems. This theory is based on the definition of a linearized characteristic equation that represents the physical behavior of each component. The physical structure of the system described by its energy interrelationships is called “primal”, and its derivatives are the costs and consumptions. The obtained cost structure is the mathematical “dual” of its primal. The theory explains why the F and P cost assessment rules and any other suggestion may (or may not be) rational under a given disaggregation scheme. A result of the theory is a new thermodynamic function called the relative free energy and a new parameter called deterioration temperature, which due to a component’s deterioration cause and is characterized by an h–s thermodynamic trajectory describing the effects on the exiting stream. The relative free energy function allows for an exact relationship between the amount of used resources and the increase in entropy generation caused by the deterioration path of the component. This function allows the obtaining of, for the first time, an appropriate characteristic equation for a turbine and a new definition of efficiency that does not depend on the environmental temperature, but on the deterioration temperature. In addition, cost with relative free energy instead of exergy may open a new path for more precise and straightforward assessments of component deterioration.