Abstract
The present paper contains an analysis of alternative functions to describe chemical equilibrium. In particular we show the equivalence of equilibrium criteria based on pressure, volume and temperature, and corresponding constraints, with respect to those popularly used in thermodynamics, i.e. those based on the minimization of internal energy, enthalpy, Helmholtz and Gibbs potentials. The analysis emphasizes the role of mathematical virtual procedures in determining the equilibrium conditions and the irrelevance of physico-chemical transformations that bring the system into the equilibrium state. Different examples, including a new derivation of Saha’s equation, are dealt with to validate this conceptual approach.
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Minimization (Min) and maximization (Max) of the relevant equations depends on the sign appearing before the term ∑ μ i dN i . This point can be also understood taking into account the inequality nature of Eq. (1) from classical thermodynamics. As an example Eq. (3) can be written as (dG) ≤ Vdp − SdT + ∑μ i dN i implying (dG) p,t ≤ ∑μ i dN i ≤ 0 Min; (dp) g,t ≥ ∑μ i dN i ≥ 0 Max; (dT) g,p ≤ ∑μ i dN i ≤ 0 Min. In this context we note that the inequality for the volume without the chemical term i.e. \(dV\leq {TdS \over p}-{dV \over p}\) was first derived by Maxwell as reported by L. C. Wood Thermodynamic Inequalities in Gases and Magnetoplasmas, J. Miley, New York 1995.
Note the second member of Eqs. (17) and (18) of Ref. 10 should be divided by RT.
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This paper is dedicated to the memory of one of the authors, Giuseppe Petrella, who unfortunately is not with us any more.
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Capitelli, M., Longo, S., Petrella, G. et al. Equivalent Potential Functions to Calculate Thermodynamic Equilibria*. Plasma Chem Plasma Process 25, 659–675 (2005). https://doi.org/10.1007/s11090-005-6819-7
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DOI: https://doi.org/10.1007/s11090-005-6819-7