Math 2.0

Classical thermodynamics, heat transfer Definition

Phase diagram

Builds on Phase transitionChemical potentialThermodynamic equilibriumIntensive and extensive properties

Definition

Consider a pure substance that can exist in phases α1,…,αk\alpha_1, \dots, \alpha_k (in the sense of phase transition). For each phase αi\alpha_i, let μi(T,p)\mu_i(T, p) be its chemical potential as a function of the temperature TT and the pressure pp. The phase diagram of the substance is the (T,p)(T, p) plane with each point labelled by certain phases. The labels of (T,p)(T, p) are the phases αi\alpha_i for which μi(T,p)\mu_i(T, p) is the smallest of μ1(T,p),…,μk(T,p)\mu_1(T, p), \dots, \mu_k(T, p). These are the phases present in thermodynamic equilibrium at (T,p)(T, p).

Remarks

A point labelled by one phase lies in a region of that phase. A point labelled by two phases lies on a coexistence curve, where the two chemical potentials are equal. A point labelled by three phases is a triple point. For water, the point T=298.15 KT = 298.15\,\mathrm{K}, p=101.325 kPap = 101.325\,\mathrm{kPa} is labelled liquid, because liquid water has the smallest chemical potential there. A non-example: labelling each point by the phase of largest molar volume does not give the phase diagram. At room conditions that rule would pick vapour, while the phase of least chemical potential of water there is liquid. For mixtures one also uses compositions as axes, together with other intensive variables such as the mole fractions.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

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Chemical potential, concept, no evidence levelChemical potentialconceptIntensive and extensive properties, concept, no evidence levelIntensive and extensi…conceptPhase transition, concept, no evidence levelPhase transitionconceptThermodynamic equilibrium, concept, no evidence levelThermodynamic equilib…conceptPhase diagram, definition, no evidence levelPhase diagramdefinition
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  1. Chemical potential concept
  2. Intensive and extensive properties concept
  3. Phase transition concept
  4. Thermodynamic equilibrium concept
  5. Phase diagram definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Phase_diagram
About this page
TagP70TC56SXN
URIm2://P70TC56SXN
Kinddefinition
WritingW0 stub
MSC80A22, 82B26, 80A10
DefinesPhase diagram
UsesPhase transition, Chemical potential, Thermodynamic equilibrium, Intensive and extensive properties
Changed3 November 2026

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