Joule–Thomson effect

The Joule–Thomson (or Joule–Kelvin) effect is the temperature change of a real gas forced through a porous plug or throttle from high to low pressure with no work extracted and no heat exchanged. The process conserves enthalpy, and the figure of merit is the Joule–Thomson coefficient μ_JT = (∂T/∂P)_H. Since the pressure always falls across the plug, a positive μ_JT means the gas cools and a negative one means it warms.

The effect exists only because gases are not ideal. An ideal gas throttled this way emerges at exactly the same temperature: its enthalpy depends on temperature alone, and the enthalpy has not changed. For a van der Waals gas, μ_JT ≈ (2a/RT − b)/C_p — a tug-of-war between molecular attraction (the a term), which cools the expanding gas because molecules must climb out of each other's attractive wells at the expense of kinetic energy, and molecular volume (the b term), which does the reverse. Because a enters divided by T, attraction wins when the gas is cold and loses when it is hot.

The temperature at which they cancel, T_inv = 2a/(Rb), is the inversion temperature, and it dictated the entire history of liquefaction. Air's is around 600 K, so Linde could throttle room-temperature air directly and build an industry on it. Hydrogen's is about 205 K and helium's about 45 K — both below room temperature — so throttling them warm merely heats them. Each had to be pre-cooled below its own inversion point by the previous cryogen in the cascade before its throttle would work at all. The same throttling appears, unglamorously, as the capillary tube in every domestic refrigerator.

James Prescott Joule and William Thomson (Lord Kelvin) performed the porous-plug experiments between 1852 and 1862, refining Joule's earlier free-expansion work, which had been too insensitive to detect the effect. Carl von Linde and William Hampson independently turned it into industrial air liquefaction in 1895 by adding a counter-current heat exchanger, which lets the apparatus bootstrap itself to cryogenic temperatures. James Dewar used it, with pre-cooling, for hydrogen in 1898, and Kamerlingh Onnes for helium in 1908.