Rethinking the phase rule and degrees of freedom. My third article on the 150th anniversary of Gibbs’s masterpiece
Abstract
This article is a detailed development of the articles published in the IV. issues of the same journal in 2024 and 2025 in one possible direction. The six essential elements of the rethinking of the phase rule and degrees of freedom are: a) the maximum number of phases that can maintain equilibrium with each other in a system is the sum of the number of components and the number of independent noncompositional state variables( e.g., pressure, temperature, but there may be others); b) the degree of freedom is the maximum number of phases thus determined minus the number of phases present in the system, or the number of parameters determining the chemical potentials minus the number of equations ensuring heterogeneous equilibrium; c) the degree of freedom is equal to the number of independent state variables that can be freely changed (at least within a finite range of values) without changing the equilibrium state of the system, i.e. the number of equilibrium phases, their nature and their equilibrium phase ratios; d) if at a special point of the phase diagram the compositions of two phases are the same (which is not typical), then the value of the degree of freedom at this (and only this) special point must be reduced by the number of these independent matches; e) the number of theoretically determinable equilibrium phase ratios in a system is equal to the number of components; if more phases are present, then the phase ratios of the other phases can be freely set by the engineer through the enthalpy and/or volume of the system; f) if mathematical rules are imposed between the average concentrations of the components to represent a 2D section of a multi-component phase diagram, this does not change either the maximum number of phases or the number of degrees of freedom; however, in this case the maximum degree of freedom will be greater than the number of independent state variables, but this only means that the given 1-phase concentration range (which corresponds to the maximum degree of freedom) is wider than what is shown on the given phase diagram section, i.e. its stability range extends along the state variables not shown on the phase diagram section. It is also stated that artificial intelligence is not intelligent, it only searches fast.
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