Abstract
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.
Highlights
The aim of this paper is challenging since it questions all the concepts that have been traditionally used in thermoeconomics, called exergoeconomics by other authors [1]
Based on its definition, the exergy cost depends on the plant disaggregation scheme
The structural theory formally relates to the input–output theory [20]; the characteristic equation makes the difference because it deeply connects the thermodynamic behavior of an energy system to the stream costs such as in a transparent box
Summary
The aim of this paper is challenging since it questions all the concepts that have been traditionally used in thermoeconomics, called exergoeconomics by other authors [1]. This would mean that environmental conditions would, for sure, influence the industrial system, not because of an arbitrary designer’s selection, but through the environment’s own natural interaction with the process If this were possible, we could give a rigorous answer to the thermodynamics of energy systems but to the economics itself, and all without leaving the Second Law. Linking the concept of cost with thermodynamics is to bridge the gap between Physics and Economics. These decisions are mainly the cost allocation rules, the level of aggregation, the fuel/product/waste definitions, and the exergy function and the reference state This will allow discerning mathematical reasons from reasonable assumptions and go forward to a new thermodynamic function: the relative free energy function
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