Math 2.0

Classical thermodynamics, heat transfer Equations of state and phases Fact

Charles's law

Builds on Ideal gas lawIdeal gasIsobaric processThermodynamic temperatureThermal expansion coefficient

Statement

Let a fixed amount of an ideal gas be kept at a fixed pressure. Then its volume VV is proportional to its thermodynamic temperature TT: VT=const,\frac{V}{T} = \text{const}, so that for any two such states V1/T1=V2/T2V_1 / T_1 = V_2 / T_2.

Remarks

It is the special case pp and nn fixed of the ideal gas law pV=nRTpV = nRT, and it describes the states of an isobaric process of an ideal gas. Example: a balloon holding 2 L2\,\mathrm{L} of air at 300 K300\,\mathrm{K}, warmed to 330 K330\,\mathrm{K} at constant pressure, expands to 2.2 L2.2\,\mathrm{L}. The temperature must be absolute: in degrees Celsius the volume is not proportional to the temperature, but it is an affine function of it. Extrapolating the straight lines V(T)V(T) of different gases to V=0V = 0 gives the same point, the absolute zero T=0T = 0, which was historically one route to the absolute temperature scale.

Going deeper

For a student

Charles's law, Boyle's law and Avogadro's law each fix two of the four quantities pp, VV, TT, nn and relate the other two; together they give pV=nRTpV = nRT. Its form is the reason the thermal expansion coefficient of an ideal gas is α=1/T\alpha = 1/T. For real gases it holds only approximately, and well only at low pressure.

Reading path

To understand this page from the ground up, read these 9 pages in order. The foundations come first.

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Equation of state, concept, no evidence levelEquation of stateconceptIdeal gas, concept, no evidence levelIdeal gasconceptIsobaric process, concept, no evidence levelIsobaric processconceptThermal expansion coefficient, concept, no evidence levelThermal expansion coe…conceptThermodynamic temperature, concept, no evidence levelThermodynamic tempera…conceptVirial expansion, concept, no evidence levelVirial expansionconceptvan der Waals equation, concept, no evidence levelvan der Waals equationconceptIdeal gas law, statement, no evidence levelIdeal gas lawstatementCharles's law, statement, no evidence levelCharles's lawstatement
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. Equation of state concept
  2. Ideal gas concept
  3. Isobaric process concept
  4. Thermal expansion coefficient concept
  5. Thermodynamic temperature concept
  6. Virial expansion concept
  7. van der Waals equation concept
  8. Ideal gas law statement
  9. Charles's law statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Charles's_law
About this page
TagCB9KR9S7G3
URIm2://CB9KR9S7G3
Kindstatement, fact
WritingW0 stub
MSC80A10, 82D05
StatusThis copy of the site has no build data. Run m2 status CB9KR9S7G3.
AboutIdeal gas, Isobaric process
UsesIdeal gas law, Ideal gas, Isobaric process, Thermodynamic temperature, Thermal expansion coefficient
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Changed3 November 2026

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