Critical Temperature and Liquefaction of Gases

Every real gas has a characteristic temperature, called its critical temperature ($T_c$), above which it is

physically impossible to liquefy the gas by applying pressure alone, no matter how great that pressure is. Below

the critical temperature, applying sufficient pressure will cause the gas to condense into a liquid; above it, the

gas simply becomes more and more compressed without ever separating into two distinct phases (liquid and vapour).

This means that cooling a gas below its critical temperature is a necessary first step before liquefaction by compression can succeed — pressure alone is never enough if the gas starts out above $T_c$.

Two related quantities complete the picture: the critical pressure ($P_c$) is the minimum pressure required to

liquefy the gas when it is held exactly at its critical temperature, and the critical volume ($V_c$) is the

volume occupied by one mole of the gas under these critical conditions ($T_c$, $P_c$). Together, $(T_c, P_c, V_c)$

define the critical point — the unique combination of temperature and pressure at which the distinction

between the liquid and gaseous states of a substance disappears entirely (the liquid and vapour densities become

identical).

Critical temperature values vary enormously between gases and directly determine how easily each gas can be

liquefied under everyday laboratory or industrial conditions. Carbon dioxide has $T_c = 31.1^\circ\text{C}$ —

only slightly above normal room temperature — so $\text{CO}_2$ can be liquefied simply by compressing it at or

below room temperature; this is exactly how $\text{CO}_2$ fire extinguishers and carbonated-drink cylinders store

liquid $\text{CO}_2$ under moderate pressure at ordinary temperatures. Oxygen, by contrast, has

$T_c = -118.6^\circ\text{C}$, far below room temperature. Since room temperature ($\approx 25^\circ\text{C}$) is

already well above oxygen's critical temperature, no amount of pressure applied at room temperature can liquefy

oxygen gas — oxygen must first be cooled below $-118.6^\circ\text{C}$ before compression can turn it into a

liquid, which is why liquid oxygen is produced industrially only through deep cryogenic cooling, not simple

compression.

The same reasoning explains why gases with very low critical temperatures — hydrogen ($T_c \approx -240^\circ \text{C}$), helium ($T_c \approx -268^\circ\text{C}$) — are notoriously difficult to liquefy and require extreme

cryogenic refrigeration, while gases with critical temperatures well above room temperature — ammonia …