Expanding the Exergy Calculation Methodology of Materials to Include Equilibrium Calculations of Complex Systems

Abstract Extractive metallurgists unmix complex mixtures arising either from ores and minerals or designed products and their functional materials to create high quality metals, compounds and alloys. To fully understand economic aspects of this endeavor, a deep understanding of solution chemistry is required be it solid solutions, high temperature liquid or aqueous solutions. Especially the configurational and excess entropies of a solid and liquid solution are important in this regard. For this reason, the simplified definition for calculating the exergy of non-ideal solutions as defined by Szargut is shown in this paper to be problematic. We reinterpret the equation Ex = (H–H°)-T°(S–S°), which is generally applied for the calculation of chemical and physical exergies of pure substances in the framework of solution phase thermodynamics. Here we demonstrate that it is more rigorous to use full solution chemistry for deriving the enthalpies (H and H°) and entropies (S and S°) for a particular system of given composition. The suggested approach links H, H°, S and S° rigorously, which is not necessarily the case in the Szargut methodology. Various examples show and compare different approaches using the Szargut approach in comparison with the general Ex -equation. We show with various examples, ranging from metal alloys to oxide slag systems, the discrepancies between the standard Szargut approach and the method of including non-ideal solution phase chemistry as suggested here. From the results presented here, it is evident that exergetic efficiencies may not have been correctly calculated in the literature so far, especially if systems show highly non-ideal behavior of the solution phases and exhibit non-stoichiometric intermetallic as well as other compound phases. The examples clarify the significant errors that can result if solution chemistry is not included. The ultimate objective is to formulate a rigorous pairing of H, H°, S and S° for each industrial and societal process and/or material stream to correctly calculate Ex to evaluate exergetic efficiency of processes and supply chains. Therefore, we suggest that all published exergies (e.g. by software, in publications, etc.) should be revisited to fully describe exergy flows in industrial systems, which the authors as engineers have found to be deficient. Graphical Abstract