9.0 Liquifaction of gases

Gases can be converted into liquid by two ways:

1. By compressing it at very high pressure.

2. By cooling it to a low temperature.

But experimentally it has been observed that cooling has significantly more importance than applying pressure. This is because of kinetic energy possessed by gaseous molecules at high temperature.

Hence in order to liquify a gas, it has to be cooled to a certain minimum temperature. This temperature is known as 'critical temperature ($T_c$)'.

The minimum pressure which is to be applied at critical temperature to convert a gas into liquid is known as 'critical pressure ($P_c$)'.

The volume of the gas at critical temperature and critical pressure is known as 'critical volume ($V_c$)' .

There are certain mathematical relations between these critical constants. $$\begin{equation} \begin{aligned} {T_c} = \frac{{8a}}{{27Rb}} \\ {P_c} = a/27{b^2} \\ {V_c} = 3b \\\end{aligned} \end{equation} $$