Details

The energy balance for an adiabatic throttle implies that

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The throttle does no work, and because the gas moves so quickly through the throttle, it does not have much time to transfer heat to the surroundings.

The Joule–Thomson coefficient is derived by starting with the exact differential for enthalpy:

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Since for a throttle, and the derivative of enthalpy with respect to temperature at constant pressure is the heat capacity , then:

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Rearranging, and given that the enthalpy is constant,

,

where , and is the Joule–Thomson coefficient.

Integration then relates the outlet temperature to the inlet temperature and the pressure drop:

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If , the outlet temperature is lower than the inlet temperature. If , then the outlet temperature is higher.

References

[1] J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics (2nd ed.), Upper Saddle River, NJ: Prentice Hall, 2012 p. 236.

[2] "Thermophysical Properties of Fluid Systems." (Aug 11, 2016) webbook.nist.gov/chemistry/fluid.