Math 2.0

Classical thermodynamics, heat transfer Definition

Equation of state

Builds on Thermodynamic systemThermodynamic equilibriumState functionTemperatureFundamental thermodynamic relation

Definition

Let a thermodynamic system consist of a fixed amount nn of a single substance. Let its equilibrium states be described by the state functions pressure pp, volume VV and temperature TT. An equation of state of the substance is a relation F(p,V,T,n)=0F(p, V, T, n) = 0 that holds in every equilibrium state. Here FF is a function such that, at fixed nn, any two of pp, VV, TT determine the third, at least locally.

Remarks

Often the relation is solved for the pressure, p=p(T,V,n)p = p(T, V, n), or written in molar form with Vm=V/nV_m = V/n. More generally, any relation between state variables of a system in equilibrium is called an equation of state. For example, U=U(T,V)U = U(T, V) is the caloric equation of state, and p=p(T,V)p = p(T, V) the thermal one. A thermal equation of state alone does not determine all thermodynamic properties; the fundamental thermodynamic relation of a substance does, and it implies all its equations of state.

Example: the ideal gas law pV=nRTpV = nRT, with the gas constant RR, is the equation of state F=pV−nRT=0F = pV - nRT = 0. Given TT and VV, it gives p=nRT/Vp = nRT/V.

Non-example: the first law dU=δQ−δWdU = \delta Q - \delta W is not an equation of state. It holds for every substance, it involves heat and work, which are not state functions, and it does not relate pp, VV, TT in equilibrium.

Reading path

To understand this page from the ground up, read these 26 pages in order. The foundations come first.

Show the path as a graph
Entropy, concept, no evidence levelEntropyconceptHeat, concept, no evidence levelHeatconceptHeat capacity ratio, concept, no evidence levelHeat capacity ratioconceptHeat engine, concept, no evidence levelHeat engineconceptIdeal gas, concept, no evidence levelIdeal gasconceptInternal energy, concept, no evidence levelInternal energyconceptIsentropic process, concept, no evidence levelIsentropic processconceptIsothermal process, concept, no evidence levelIsothermal processconceptReversible process, concept, no evidence levelReversible processconceptState function, concept, no evidence levelState functionconceptTemperature, concept, no evidence levelTemperatureconceptThermal efficiency, concept, no evidence levelThermal efficiencyconceptThermodynamic cycle, concept, no evidence levelThermodynamic cycleconceptThermodynamic equilibrium, concept, no evidence levelThermodynamic equilib…conceptThermodynamic system, concept, no evidence levelThermodynamic systemconceptThermodynamic temperature, concept, no evidence levelThermodynamic tempera…conceptThermodynamic work, concept, no evidence levelThermodynamic workconceptClausius statement of the second law, statement, no evidence levelClausius statement of…statementFirst law of thermodynamics, statement, no evidence levelFirst law of thermody…statementKelvin–Planck statement of the second law, statement, no evidence levelKelvin–Planck stateme…statementCarnot's theorem, statement, no evidence levelCarnot's theoremstatementCarnot cycle, example, no evidence levelCarnot cycleexampleClausius theorem, statement, no evidence levelClausius theoremstatementSecond law of thermodynamics, statement, no evidence levelSecond law of thermod…statementFundamental thermodynamic relation, statement, no evidence levelFundamental thermodyn…statementEquation of state, definition, no evidence levelEquation of statedefinition
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. Entropy concept
  2. Heat concept
  3. Heat capacity ratio concept
  4. Heat engine concept
  5. Ideal gas concept
  6. Internal energy concept
  7. Isentropic process concept
  8. Isothermal process concept
  9. Reversible process concept
  10. State function concept
  11. Temperature concept
  12. Thermal efficiency concept
  13. Thermodynamic cycle concept
  14. Thermodynamic equilibrium concept
  15. Thermodynamic system concept
  16. Thermodynamic temperature concept
  17. Thermodynamic work concept
  18. Clausius statement of the second law statement
  19. First law of thermodynamics statement
  20. Kelvin–Planck statement of the second law statement
  21. Carnot's theorem statement
  22. Carnot cycle example
  23. Clausius theorem statement
  24. Second law of thermodynamics statement
  25. Fundamental thermodynamic relation statement
  26. Equation of state definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Equation_of_state
About this page
TagE9EHPV3N8V
URIm2://E9EHPV3N8V
Kinddefinition
WritingW0 stub
MSC80A10, 76N15, 82D05
DefinesEquation of state
UsesThermodynamic system, Thermodynamic equilibrium, State function, Temperature, Fundamental thermodynamic relation
Changed3 November 2026

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • 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

No page links to this page yet.