Liquefaction of gases

Storing gases as liquids matters enormously in practice -- LPG cylinders and rocket propellants are two everyday examples where a gas must be handled in its far more compact liquid form. The standard liquefaction methods are all built on a single underlying phenomenon: the Joule-Thomson effect.

When a compressed gas is forced through a small orifice or porous plug into a region of lower pressure, it expands adiabatically (no heat exchanged with the surroundings) -- and, for most gases under most conditions, this expansion produces an appreciable cooling. This lowering of temperature on adiabatic expansion from high pressure to low pressure through a throttling device is the Joule-Thomson effect.

The effect is only observed below a temperature specific to each gas, called its inversion temperature ($T_i$), given in terms of the van der Waals constants by

Below $T_i$, throttling a gas cools it; exactly at $T_i$, throttling produces no temperature change at all; and above $T_i$, the same throttling expansion actually heats the gas instead of cooling it. Gases with a low critical temperature -- O$_2$, He, N$_2$, H$_2$ -- are the ones for which the Joule-Thomson effect can be exploited effectively for cooling and liquefaction in practice.

Three practical liquefaction methods build on this:

1. Linde's method uses the Joule-Thomson effect directly and repeatedly to liquefy air or another gas. …