# Liquefaction of Gases

Gases liquify by the combined effect of compression (pressure) and cooling (temperature) By applying low temperature, the Kinetic Energy of molecules decrease and get closer till they change to liquid. So also high pressures brings the gas molecules closer so as to permit attractive forces to be large enough to change to liquids.

Thomas Andrews did notable work on liquefaction of gases, like carbon dioxide. According to him there exists for each gas a certain temperature, called critical temperature, above which it cannot be liquefied, no matter how large, the pressure applied is. For example for CO2 304.15 K is the critical temperature (Tc), for H2 it is 33.2, for N2 it is 126 K etc.

The minimum pressure necessary to liquify any gas at its critical temperature is called critical pressure (Pc) and corresponding volume, occupied by one mole of gas is called critical volume (Vc)

The following is the Andrew's isotherms of CO2.

Andrews studied the pressure-volume relation of CO2 at different temperatures and his results are shown in Figure. The isotherm T7 represents the data obtained at a relatively high temperature. Its form is very close to that of a rectangular hyperbola and shows that at this temperature CO2 follows Boyle's law rather closely.

Now consider the isotherm T1 that is below the critical point. As the vapour is compressed, the P-V curve follows, AB, which is roughly in accordance with Boyle's law. When the point B is reached liquid CO2 is formed and this can be observed by the appearance of a meniscus between vapour phase and liquid phase and liquid phase. As the volume decreases further, more of the gas is transferred to the liquid phase while the pressure remains constant (note the flat portion of the curve). Finally at C all of the CO2

is in the liquid phase and the curve CD is the isotherm of liquid CO2. Since the liquids are relatively incompressible, the compression of the liquid from C to D results in little volume change and hence the curve CD is very steep.
The flat part of the isotherm reveals an important fact that as long as both liquid and gas phases are present, the pressure of the gas in contact with the liquid must be the same, quite independent of whether a small or a large fraction of the volume is occupied by liquid. This equilibrium pressure is known as the vapour pressure of the liquid at that particular temperature. As isotherms are taken at successively higher temperature we find that the flat part, i.e. the volume range in which the phases co-exist, becomes shorter and shorter until for a particular isotherm (T5) its length is reduced to zero at the point 'P'. This is the critical point and the isotherm on which it lies is the critical isotherm. This temperature is known as the critical temperature. The observations of Andrews regarding CO2 are generally valid for all other gases.