Math 2.0

Classical thermodynamics, heat transfer Definition

Triple point

Builds on Phase diagramChemical potentialThermodynamic equilibrium

Definition

Let a pure substance have phases with chemical potentials μ1(T,p),…,μk(T,p)\mu_1(T, p), \dots, \mu_k(T, p). A triple point of the substance is a pair (T,p)(T, p) at which three distinct phases α,β,γ\alpha, \beta, \gamma satisfy μα(T,p)=μβ(T,p)=μγ(T,p)=min⁡1≤i≤kμi(T,p).\mu_\alpha(T, p) = \mu_\beta(T, p) = \mu_\gamma(T, p) = \min_{1 \le i \le k} \mu_i(T, p). Then the three phases coexist in thermodynamic equilibrium.

Remarks

In the phase diagram, a triple point is a point labelled by three phases. Water has a triple point of ice, liquid and vapour at T=273.16 KT = 273.16\,\mathrm{K} and p≈611.657 Pap \approx 611.657\,\mathrm{Pa}. A non-example: the normal melting point of ice, T=273.15 KT = 273.15\,\mathrm{K} and p=101.325 kPap = 101.325\,\mathrm{kPa}, is not a triple point. Only ice and liquid have the minimal chemical potential there; vapour is not stable at that pressure. A substance can have several triple points; water has more, which involve different crystalline forms of ice.

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  1. Chemical potential concept
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  3. Thermodynamic equilibrium concept
  4. Triple point definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Triple_point
About this page
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Kinddefinition
WritingW0 stub
MSC80A22, 80A10
DefinesTriple point
UsesPhase diagram, Chemical potential, Thermodynamic equilibrium
Changed3 November 2026

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