Every student of thermodynamics grasps entropy growth in terms of dissipation of energy. The real nature of energy and entropy is subtle. This critical review of the evolution of thermodynamic thought uncovers the remarkable advance on our understanding of energy made by Kelvin with his dissipation of energy proposition. Maxwell and Planck, however, pointed out that dissipation of energy does not exhaust growth of entropy (i.e., the idea of spontaneity), and in fact, as it is shown here, Kelvin’s proposition of dissipation of energy (1852) is subsumed under the principle of the increase of entropy (Clausius, 1865). It is necessary, therefore, for thermodynamics to become a coherent conceptual system, to introduce spontaneity as an independent concept. Instead of the heat-work dyad framework, the introduction of spontaneity entails energy transformation to be viewed in terms of a triad framework of heat (from the reservoir)-work-spontaneity. Spontaneity is the new energy in the triad framework, and it is also clear that energy commodity (fungible energy or energy carriers) is only one kind of spontaneity, stock spontaneity; the other kind is ongoing spontaneity, the consideration of which is necessary for comprehending problems of homeostasis in both the organic and inorganic worlds. 1. Introduction William Thomson (later Lord Kelvin) established energy, alongside force, as a central concept in physics as well as everyday life by his formulation of the principle of dissipation of energy [1]. This principle has been identified with the principle of the increase of entropy formulated by Clausius [2, 3]. However, how the two principles are used suggests otherwise. The Kelvin treatment has evolved into the related concept of exergy1 (see Note 1 and [4] for definition of exergy) or maximum useful work. And the Clausius treatment has been developed by Gibbs into the Clausius-Gibbsian equilibrium thermodynamics. Whereas the Kelvinian ideas of energy and exergy dissipation are extremely useful, the Clausius concepts of entropy and entropy production are in fact the basic ones: “dissipation of mechanical energy” [1, pp. 511–514] is only one example of tendencies in entropy production or spontaneity,2 albeit the most important one as Kelvin defined it (see below); even so, a whole perspective is possible only if thermodynamics is understood in terms of both energy dissipation and entropy growth—the former spontaneous and the latter universal. Here we show that the concept of maximum useful work is subsumed under the entropy law and, thereby, thermodynamics becomes
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On page 298 of [4], the definition of exergy is given as “The maximum fraction of an energy form which (in a reversible process) can be transformed into work is called exergy. The remaining part is called anergy, and this corresponds to the waste heat.”
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On pp. 103-104 of [18, Planck, (1969). Treatise on Thermodynamics, 3rd edition. (Dover)], Planck wrote, The real meaning of the second law has frequently been looked for in a “dissipation of energy.” This view, proceeding, as it does, from the irreversible phenomena of conduction and radiation of heat, presents only one side of the question. There are irreversible processes in which the final and initial states show exactly the same form of energy, for example, the diffusion of two perfect gases (Section 238), or further dilution of a dilute solution. Such processes are accompanied by no perceptible transference of heat, nor by external work, nor by any noticeable transformation of energy. They occur only for the reason that they lead to an appreciable increase of the entropy.
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Maximum useful work derived from isolate systems, therefore, decreases with decreasing reservoir temperature according to (15). But, because is a function of , the dependency of maximum useful work on in (9) is not straightforward. Every student of thermodynamics knows that work increases with decreasing , which results from greater increase in overcompensating decrease in . Every student also knows that work increases with increasing “peak cycle temperature” according to (3), which is a special case of (9). The general prediction of (9), however, is more subtle and includes the possibility of work being independent of peak cycle temperature for the case of reversible “combustion” cycle—which is consistent with the idea of Gibbs free energy [31].
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