Liquifaction of Gases

Andrews' isotherms of carbon dioxide

The first complete picture of how pressure, volume and temperature relate together in both the gaseous and liquid states of a substance came from Thomas Andrews, who plotted isotherms of carbon dioxide at several temperatures (Fig. 5.13); real gases in general were later found to behave just like CO$_2$ does here.

At high temperatures, the isotherms resemble those of an ideal gas, and no amount of pressure can liquefy the gas. As temperature is lowered, the curves start to deviate noticeably from ideal shape. At 30.98 $^{\circ}$C, CO$_2$ stays gaseous up to 73 atmospheres (point E) — at that pressure, liquid CO$_2$ appears for the very first time. This temperature, 30.98 $^{\circ}$C, is CO$_2$'s critical temperature ($T_C$) — the highest temperature at which liquid CO$_2$ can exist; above it, only gas is possible, however much pressure is applied. The volume of one mole of gas at the critical temperature is the critical volume ($V_C$), and the corresponding pressure is the critical pressure ($p_C$) — together, $T_C$, $p_C$, $V_C$ are the critical constants. Beyond this point, further pressure merely compresses the already-liquid CO$_2$, seen as a very steep line — liquids are barely compressible.

Below the critical temperature

At a cooler temperature such as 21.5 $^{\circ}$C, CO$_2$ remains a pure gas only up to point B; from B onward, liquid of a definite volume starts to appear, and further compression does not raise the pressure at all — instead, more and more gas simply condenses into liquid, at constant pressure, until point C, where all the gas has condensed. Beyond C, the curve again turns steep, since we are now compressing pure liquid. This same pattern — a flat, horizontal "condensation plateau" — appears at every temperature below $T_C$, with the plateau growing longer at lower temperatures, and shrinking to a single point exactly at the critical temperature.

A point like A represents pure gas; a point like D represents pure liquid; any point under the dome-shaped region represents liquid and gas coexisting in equilibrium.

Table 5.4 lists critical constants for some common substances:

Liquefying "permanent" gases, and the continuity of gas and liquid

All gases show the same qualitative behaviour as CO$_2$ under isothermal compression — every gas must be cooled below its critical temperature before it can be liquefied at all; gases that show a strong, continuous positive deviation from ideality (the "permanent gases") need both substantial cooling and considerable compression, since compression brings molecules close together while cooling slows them down enough for intermolecular attraction to hold them there. …