Abstract
This article shows that the Gibbs function topological manifold \(G(p,T,x_{1}, x_{2},\ldots ,x_{C})\) at the thermodynamic equilibrium is always two-dimensional (2D). This means that the set of values \(G\), regardless of the number of independent components \(C\), creates a 2-D surface. Based on a state with zero degrees of freedom as a reference state, it was shown that the state of a thermodynamic equilibrium is represented by a graph on such a 2-D surface. In the equilibrium state, graph edges that connect points corresponding to individual degrees of freedom have a minimal length.
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Notes
about congruent and non-congruent processes in [19] we can read: if “the components form a compound stable up to the melting point” then “the compound melts at a constant temperature and the melt has the same stoichiometric composition; such compounds are said to have congruent melting points” and if “the components form a compound unstable at the melting point” then it “decomposes below its melting point, which on further heating forms a melt with a composition different from that corresponding to the stoichiometry of the compound. These compounds are said to have incongruent (non-congruent) melting point.”
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In memory of Marysia Ajzensztadt (1922–1942), the Nightingale of the Warsaw Ghetto.
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Turulski, J. Dimension of the Gibbs function topological manifold: 1. Graph representation of the thermodynamic equilibrium state. J Math Chem 53, 495–513 (2015). https://doi.org/10.1007/s10910-014-0439-5
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DOI: https://doi.org/10.1007/s10910-014-0439-5