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 costing 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 due to a component’s deterioration cause, characterized by a 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 environment temperature but on its deterioration temperature. Also, costing with relative free energy instead of exergy may open a new path for more precise and straightforward assessments of component deteriorations.

Antonio Valero Capilla and César Torres Cuadra

2020

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 costing 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 due to a component’s deterioration cause, characterized by a 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 environment temperature but on its deterioration temperature. Also, costing with relative free energy instead of exergy may open a new path for more precise and straightforward assessments of component deteriorations.

Antonio Valero Capilla and Alicia Valero Delgado interviewed by Adrián Almazán

We need a material transition, not only energetic, that restores nature and effectively reuses materials. Gaia must be cared for by extending life on Earth and slowing its degradation towards Thanatia.

Thermodynamics for Sustainable Management of Natural Resources

Wojciech Stanek (Editor)

This book examines ways of assessing the rational management of nonrenewable resources. Integrating numerous methods, it systematically exposes the strengths of exergy analysis in resources management.

Thanatia: The Destiny of the Earth's Mineral Resources

A Thermodynamic Cradle-to-Cradle Assessment by (author): Antonio Valero Capilla and Alicia Valero Delgado

Is Gaia becoming Thanatia, a resource exhausted planet? For how long can our high-tech society be sustained in the light of declining mineral ore grades, heavy dependence on un-recycled critical metals and accelerated material dispersion? These are all root causes of future disruptions that need to be addressed today.