Revisiting Exergy and Chemical Potential Concepts

In this presentation, I will revisit a few topics in thermodynamics. One is exergy and the other is chemical potential. Exergy (also called availability) represents the maximum useful work possible when a system at a specific state reaches equilibrium with the environmental dead state at temperature T_o. If the process involves irreversibility, the Guoy-Stodola theorem states that the exergy destruction equals the entropy generated during the process multiplied by T_o. The exergy concept and the Gouy-Stodola theorem are widely used to optimize processes or systems, even when they are not directly connected to the environment. In the past, questions have been raised on if T_o is the proper temperature to use in calculating the exergy destruction. We start from the first and the second laws of thermodynamics to unambiguously show that the useful energy loss (UEL) of a system or process should equal to the entropy generation multiplied by an equivalent temperature associated with the entropy rejected out of the entire system. By following the entropy flow, we resolve the controversy over the definition of fuel efficiency and generalize the Carnot efficiency expression that can be applied to fuel cells. We argue that the UEL should be used for system optimization rather than the exergy destruction, and give examples on how to apply the concept to optimize thermal systems. Next, we move on to discuss chemical potential, which is the driving force for mass and charge transfer. We will first show that the well-established Donnan equilibrium had missed the pressure dependence of the chemical potential. Including this dependence leads to the coupling of Donnan potential with the osmotic pressure. It turns out that both the Guoy-Chapman theory for the electrical double layer and the Nernst-Planck charge transport theory neglect this coupling too, leading to some difficulties in the theories. I will finally comment why current ways of calculating the chemical potential based on listed properties, such as steam table for water, is problematic.

References
Y. Tu and G. Chen, “Rethinking loss of available work and Guoy-Stodola theorem,” ASME Journal of Heat Transfer, in press.
G. Chen, “Donnan equilibrium revisited: coupling between ion concentrations, osmotic pressure, and Donnan potential,” J. Micromechanics and Molecular Physics, 7, 127-134, 2022.