This temperature below which a gas obey Joule Thomson effect is called inversion temperature (T_i).At the inversion temperature, no rise or fall in temperature of a gas occurs while expanding. But above the inversion temperature, the gas gets heated up when allowed to expand through a hole. It is related to Vander Waals equation by 
\({ T }_{ i }=\frac { 2a }{ Rb } \)

(i) At the temperature of 31°C CO₂ remains as a gas and below this temperature, CO₂ can be converted to a liquid. Thus, this temperature is called critical temperature. Above this temperature, CO₂ exists mainly as a gas.
(ii) The pressure required to liquefy a gas at its critical temperature is known as critical pressure. For CO₂, it is 73 atm.
(iii) The volume occupied by one mol of CO₂ at its critical temperature and critical pressure is known as critical volume.

\(Z=\frac { { PV }_{ real } }{ nRT } \) ......(1)
\({ V }_{ ideal }=\frac { nRT }{ P } \)  ......(2)
Substituting (2) in (1)
\(Z=\frac { { V }_{ real } }{ { V }_{ ideal } } \)
Where V_real is the molar volume of the real gas and ideal is the molar volume of it when it behaves ideal. i.e. compressibility is the ratio of real volume of the. gas to ideal volume of any gas.

(i) Boyle's point is the temperature at which, real gases behave ideally over a range of low pressures.
(ii) The Boyle point varies with the nature of the gas.
(iii) Above the Boyle point, Z > 1 for real gases. i.e., they show positive deviation.
(iv) Below the Boyle point, the real gases first show a decrease for Z, reaches a minimum and then increase with increase in pressure.

Compressibility factor is the ratio of PV to nRT.
Z = \(\frac{PV}{nRT}\)
For ideal gases PV = nRT i.e., Z = 1
At high pressures Z > 1 (Positive deviation)
At inter mediate pressures Z < 1 (negative deviation)