Math 2.0

Classical thermodynamics, heat transfer Laws of thermodynamics Fact

Nernst heat theorem

Builds on EntropyThermodynamic temperatureIsothermal processThermodynamic equilibriumGibbs free energyEnthalpy

Statement

Let a system in internal equilibrium undergo an isothermal process at thermodynamic temperature TT between two equilibrium states. Let ΔS(T)\Delta S(T) be the change of its entropy in this process. Then ΔS(T)→0\Delta S(T) \to 0 as T→0+T \to 0^+.

Remarks

Walther Nernst first stated it for chemical reactions between condensed phases. In that form it says that the changes of Gibbs free energy and enthalpy of the reaction satisfy ΔG−ΔH=−T ΔS→0\Delta G - \Delta H = -T \, \Delta S \to 0 faster than TT. So the curves of ΔG\Delta G and ΔH\Delta H against TT meet at T=0T = 0 with a common horizontal tangent. The theorem is a postulate supported by experiment, and quantum statistical mechanics explains it when the ground state is not degenerate. It fails for systems that are not in internal equilibrium, such as glasses, which keep a residual entropy.

Going deeper

For a student

The Nernst heat theorem is one form of the third law of thermodynamics. It allows absolute values of entropy to be assigned, so that equilibrium constants of reactions can be computed from heat measurements alone. It also implies that heat capacities tend to 00 as T→0+T \to 0^+.

Reading path

To understand this page from the ground up, read these 7 pages in order. The foundations come first.

Show the path as a graph
Enthalpy, concept, no evidence levelEnthalpyconceptEntropy, concept, no evidence levelEntropyconceptGibbs free energy, concept, no evidence levelGibbs free energyconceptIsothermal process, concept, no evidence levelIsothermal processconceptThermodynamic equilibrium, concept, no evidence levelThermodynamic equilib…conceptThermodynamic temperature, concept, no evidence levelThermodynamic tempera…conceptNernst heat theorem, statement, no evidence levelNernst heat theoremstatement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Enthalpy concept
  2. Entropy concept
  3. Gibbs free energy concept
  4. Isothermal process concept
  5. Thermodynamic equilibrium concept
  6. Thermodynamic temperature concept
  7. Nernst heat theorem statement

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Nernst_heat_theorem
About this page
Tag9MVG566SX3
URIm2://9MVG566SX3
Kindstatement, fact
WritingW0 stub
MSC80A05, 80A10
StatusThis copy of the site has no build data. Run m2 status 9MVG566SX3.
AboutEntropy
UsesEntropy, Thermodynamic temperature, Isothermal process, Thermodynamic equilibrium, Gibbs free energy, Enthalpy
Same as
Changed3 November 2026

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (0 of 1)
  • a source with a locator (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

Used by