Phase rule

Gibbs’s phase rule relates the degrees of freedom of a system at thermodynamic equilibrium to its number of components and phases.

Gibbs phase rule: The equation F = C − P + 2, relating degrees of freedom F, components C, and phases P at equilibrium. This is the standard form of the phase rule for nonreacting systems.
Phase diagram: A graph showing which phases are stable under specified conditions such as temperature, pressure, and composition. The phase rule predicts the dimensionality of regions and boundaries in such diagrams.
Thermodynamic equilibrium: A state in which macroscopic flows of matter and energy cease and thermodynamic properties remain stable. Gibbs’s relation applies only when the phases have reached mutual equilibrium.
Josiah Willard Gibbs: An American mathematical physicist whose work established foundations of statistical mechanics and chemical thermodynamics. Gibbs derived the phase rule as part of his analysis of heterogeneous systems.
Degrees of freedom (thermodynamics): The number of independent intensive variables that can be changed without changing the number of phases in equilibrium. The phase rule’s left-hand side counts these independently variable conditions.
Triple point: A condition at which three phases of a substance coexist in thermodynamic equilibrium. For a one-component system, three phases leave zero degrees of freedom under the rule.
Intensive and extensive properties: Thermodynamic properties are intensive when independent of system size and extensive when proportional to it. The phase rule counts intensive variables rather than amounts of material.
On the Equilibrium of Heterogeneous Substances: Gibbs’s two-part treatise, published in 1876 and 1878, developing a general theory of thermodynamic equilibrium. The phase rule emerged from this systematic treatment of multiphase systems.
Component (thermodynamics): A minimum independent set of chemical constituents needed to express every phase composition in a system. The component count sets how many independent composition variables enter the rule.
Eutectic point: The composition and temperature at which a liquid alloy transforms into two solid phases simultaneously. The invariant equilibrium illustrates the phase rule in a multicomponent condensed system.

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