Math 2.0

Classical thermodynamics, heat transfer Laws of thermodynamics Fact

Third law of thermodynamics

Builds on EntropyThermodynamic temperatureThermodynamic equilibriumNernst heat theoremUnattainability principleHeat capacity

Statement

Let a system be in internal equilibrium. As its thermodynamic temperature TT tends to 0+0^+, its entropy tends to a constant S0S_0. This constant does not depend on the other state variables, such as pressure, volume or magnetic field. In Planck's form, S0=0S_0 = 0 for a perfect crystal.

Remarks

Two other common forms are the Nernst heat theorem and the unattainability principle. One consequence concerns heat capacities. Along a path at fixed external parameters, S(T)−S(T1)=∫T1TC(τ)/τ dτS(T) - S(T_1) = \int_{T_1}^{T} C(\tau) / \tau \, d\tau, where CC is the heat capacity. Since SS has a finite limit at 00, the integral must converge at 00, so CC cannot tend to a positive limit as T→0+T \to 0^+. In practice C(T)→0C(T) \to 0 as T→0+T \to 0^+. The law does not hold for glasses and other systems frozen out of equilibrium, which keep a nonzero residual entropy.

Going deeper

For a student

The third law fixes the additive constant in the entropy, which the second law leaves free. So one can speak of absolute entropies and tabulate them. It also forces heat capacities and thermal expansion coefficients to vanish at absolute zero.

Reading path

To understand this page from the ground up, read these 11 pages in order. The foundations come first.

Show the path as a graph
Adiabatic process, concept, no evidence levelAdiabatic processconceptEnthalpy, concept, no evidence levelEnthalpyconceptEntropy, concept, no evidence levelEntropyconceptGibbs free energy, concept, no evidence levelGibbs free energyconceptHeat capacity, concept, no evidence levelHeat capacityconceptIsothermal 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 theoremstatementUnattainability principle, statement, no evidence levelUnattainability princ…statementThird law of thermodynamics, statement, no evidence levelThird law of thermody…statement
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. Adiabatic process concept
  2. Enthalpy concept
  3. Entropy concept
  4. Gibbs free energy concept
  5. Heat capacity concept
  6. Isothermal process concept
  7. Thermodynamic equilibrium concept
  8. Thermodynamic temperature concept
  9. Nernst heat theorem statement
  10. Unattainability principle statement
  11. Third law of thermodynamics statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Third_law_of_thermodynamics
About this page
TagGCK4B5PSTJ
URIm2://GCK4B5PSTJ
Kindstatement, fact
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MSC80A05, 80A10
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AboutEntropy
UsesEntropy, Thermodynamic temperature, Thermodynamic equilibrium, Nernst heat theorem, Unattainability principle, Heat capacity
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Changed3 November 2026

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