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The Joule-Thomson effect

A steady throttling process is approximately isenthalpic. For a real gas, changing pressure at constant enthalpy can change temperature. This is the Joule-Thomson effect.

The Joule-Thomson coefficient is

$$\mu_{JT}=\left(\frac{\partial T}{\partial p}\right)_h.$$

If $\mu_{JT}>0$, reducing pressure at constant enthalpy lowers temperature. If $\mu_{JT}<0$, throttling raises temperature.

An ideal gas has $h=h(T)$ only, so constant enthalpy implies constant temperature and

$$\mu_{JT}=0.$$

Real gases have intermolecular interactions, so $h$ can depend on both temperature and pressure. Their Joule-Thomson coefficient changes sign across an inversion curve.

This distinction explains why throttling can be useful in gas liquefaction and refrigeration for appropriate inlet states, while the same pressure reduction may fail to cool a gas outside its cooling region.