Abstract
The paper addresses the problem of the existence and quantification of the exergy of non-equilibrium systems. Assuming that both energy and exergy are a priori concepts, the Gibbs “available energy” A is calculated for arbitrary temperature or concentration distributions across the body, with an accuracy that depends only on the information one has of the initial distribution. It is shown that A exponentially relaxes to its equilibrium value, and it is then demonstrated that its value is different from that of the non-equilibrium exergy, the difference depending on the imposed boundary conditions on the system and thus the two quantities are shown to be incommensurable. It is finally argued that all iso-energetic non-equilibrium states can be ranked in terms of their non-equilibrium exergy content, and that each point of the Gibbs plane corresponds therefore to a set of possible initial distributions, each one with its own exergy-decay history. The non-equilibrium exergy is always larger than its equilibrium counterpart and constitutes the “real” total exergy content of the system, i.e., the real maximum work extractable from the initial system. A systematic application of this paradigm may be beneficial for meaningful future applications in the fields of engineering and natural science.
Highlights
To extend equilibrium thermodynamics into the realm of real processes, the concepts of quasi-equilibrium and quasi-reversible process are customarily used: it is assumed that a system evolves in time from one state to the other through a series of very small “changes”, such that: (a) the intermediate states can be represented on an equilibrium state diagram; (b) the integral along the path produces finite amounts of thermal and/or mechanical and/or chemical effects on the system and on other systems it may interact with
It is perhaps not superfluous to underscore though that we are not interested in providing a “new” definition of the exergy of non-equilibrium systems: the question we address is really “how much work can we extract from the evolution of a system from arbitrary initial conditions to its equilibrium state”, or, reversing the problem, “how much exergy must be supplied to a system initially in equilibrium to bring it to a specified non-equilibrium state”
According to the original definition by Gibbs [20], the available energy or availability A is a thermodynamic function representing the maximum work that can be extracted from a system that proceeds from an initial arbitrary state to its final “internal” equilibrium state
Summary
This paper presents a derivation of the value of exergy for systems out of equilibrium. If the description of such processes could rely on a set of primitive thermodynamic variables known to maintain their validity under non-equilibrium conditions, their quantitative calculation could be improved and result in better designs. Complex living and non-living systems [3,4,5,6,7,8,9] would be simpler if globally valid non-equilibrium quantities were at hand Most of these references present a different approach to the problem of defining a non-equilibrium entropy. They are all well-posed, and we do not imply that there is an error in the respective formulations: we claim that our approach is simpler and leads (for macroscopic systems) to accurate results with less effort. The distinction between reversible and “invertible” processes introduced in [14] has scientific merit, but their method is very much distant from what we propose
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