Compressibility factor

The compressibility factor Z = PV/(nRT) is the ratio of a real gas's PV product to the value the ideal gas law would predict. By construction Z = 1 for an ideal gas at every pressure and temperature, so any deviation of Z from 1 is a direct, dimensionless measure of non-ideal behaviour.

Real gases trace a characteristic curve. At moderate pressure intermolecular attraction helps the molecules draw together, so the gas compresses more than ideal and Z dips below 1. At high pressure the finite size of the molecules dominates — they resist being packed — and Z rises above 1. The pressure at which Z returns to 1, and the temperature at which the low-pressure slope vanishes (the Boyle temperature), are useful fingerprints of a gas.

The factor is the practical link between the ideal gas law and equations of state such as van der Waals or the virial expansion, which express Z as a series in density. It is widely used in chemical and petroleum engineering, where accurate gas densities at high pressure matter.

Grew out of nineteenth-century studies of real-gas deviations by Regnault and Andrews; formalised through the van der Waals equation (1873) and the virial expansion of Kamerlingh Onnes (1901).