Math 2.0

Classical thermodynamics, heat transfer Definition

Joule–Thomson effect

Builds on EnthalpyAdiabatic processIrreversible processHeat capacityThermal expansion coefficientIdeal gasPartial derivative

Definition

Let a fluid flow steadily through a throttle, such as a valve or a porous plug, from pressure p1p_1 to pressure p2<p1p_2 < p_1. Assume that the flow is adiabatic, that no shaft work is done, and that the changes of kinetic and potential energy are negligible. Then the specific enthalpy is the same before and after the throttle, h1=h2h_1 = h_2; this irreversible process is the Joule–Thomson expansion. The Joule–Thomson effect is the resulting change of temperature, and the Joule–Thomson coefficient is the partial derivative μJT=(∂T∂p)H.\mu_{\mathrm{JT}} = \left( \frac{\partial T}{\partial p} \right)_H.

Remarks

A positive μJT\mu_{\mathrm{JT}} means the fluid cools on expansion, a negative one that it warms. The states where μJT=0\mu_{\mathrm{JT}} = 0 form the inversion curve in the (T,p)(T, p) plane. From dH=T dS+V dpdH = T\,dS + V\,dp and a Maxwell relation one gets μJT=VCp(Tα−1),\mu_{\mathrm{JT}} = \frac{V}{C_p} (T \alpha - 1), where CpC_p is the heat capacity at constant pressure and α\alpha the thermal expansion coefficient.

Example: for a van der Waals gas at low pressure, μJT≈1Cp,m(2aRT−b)\mu_{\mathrm{JT}} \approx \frac{1}{C_{p,m}} \left( \frac{2a}{RT} - b \right) per mole, so it cools below the inversion temperature 2a/(Rb)2a/(Rb) and warms above it.

Non-example: for an ideal gas, α=1/T\alpha = 1/T, so Tα−1=0T\alpha - 1 = 0 and μJT=0\mu_{\mathrm{JT}} = 0. Since its enthalpy depends only on temperature, constant enthalpy means constant temperature, and there is no effect.

Reading path

To understand this page from the ground up, read these 12 pages in order. The foundations come first.

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Adiabatic process, concept, no evidence levelAdiabatic processconceptEnthalpy, concept, no evidence levelEnthalpyconceptEuclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptHeat capacity, concept, no evidence levelHeat capacityconceptIdeal gas, concept, no evidence levelIdeal gasconceptIrreversible process, concept, no evidence levelIrreversible processconceptThermal expansion coefficient, concept, no evidence levelThermal expansion coe…conceptFunction of several variables, concept, no evidence levelFunction of several v…conceptLimit of a function of several variables, concept, no evidence levelLimit of a function o…conceptPartial derivative, definition, no evidence levelPartial derivativedefinitionJoule–Thomson effect, definition, no evidence levelJoule–Thomson effectdefinition
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. Euclidean space object
  4. Function concept
  5. Heat capacity concept
  6. Ideal gas concept
  7. Irreversible process concept
  8. Thermal expansion coefficient concept
  9. Function of several variables concept
  10. Limit of a function of several variables concept
  11. Partial derivative definition
  12. Joule–Thomson effect definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Joule–Thomson_effect
About this page
TagTWJ602ABBD
URIm2://TWJ602ABBD
Kinddefinition
WritingW0 stub
MSC80A10, 76N15
DefinesJoule–Thomson effect
UsesEnthalpy, Adiabatic process, Irreversible process, Heat capacity, Thermal expansion coefficient, Ideal gas, Partial derivative
Changed3 November 2026

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