Inversion Curve

a curve on a phase diagram that bounds the region of those phases (states) of a substance for which the transition of the substance from higher pressure to lower (in the process of throttling) is associated with a temperature drop. Beyond this region, the substance (a gas or liquid) heats on throttling. The constant-pressure line (isobar p = constant; see Figure 1) intersects the inversion curve at the two inversion points: the upper (T_{i, max}) and the lower (T_{i, min}). The upper point lies in the region of the gaseous state of the substance, and the lower in the liquid state.

Figure 1. Inversion curves for air in pressure-temperature coordinates calculated according to (1) the Van der Waals equation and (2) experimental data

When T_{i, min} < T < T_{i, max} in a certain interval of pressure, the gas can be liquefied by throttling, but when T > T_{i, max} this cannot be accomplished. The closer a gas is in its properties to an ideal gas, the lower its inversion temperature (for hydrogen, for example, at atmospheric pressure T_{i, max} = −57°C, while for helium, T_{i, max} = −239°C). To liquefy helium by throttling, its temperature must first be reduced to −239°C.