# Compressibility Factor

on . Posted in Dimensionless Numbers

Compressibility factor, abbreviated as Z, a dimensionless number, also called compression factor or gas deviation factor, corrects for deviation from the ideal gas law to account for the real gases behavior.  It is defined as the ratio of the actual molar volume of a gas to the molar volume predicted by the ideal gas law at the same temperature and pressure.

For an ideal gas, the compressibility factor is always equal to 1, indicating that the gas follows the ideal gas law exactly.  However, real gases can deviate from ideal behavior due to intermolecular forces, molecular size, and other factors.  As a result, the compressibility factor for real gases can be greater or less than 1.  At low pressures and high temperatures, most gases tend to behave more ideally, and their compressibility factors approach 1.  At high pressures and low temperatures, gases can exhibit significant deviations from ideal behavior, and their compressibility factors can deviate substantially from 1.

The compressibility factor is an essential parameter for accurately modeling and predicting the behavior of real gases in various thermodynamic processes and calculations, such as determining the fugacity, calculating compressibility and density, and analyzing phase equilibria.

### compressibility factor formula

$$Z \;=\; p \; V \;/\; n \; R \; T$$     (Compressibility Factor)

$$p \;=\; z \; n \; R \; T \;/\; V$$

$$V \;=\; z \; n \; R \; T \;/\; P$$

$$n \;=\; p \; V \;/\; z \; R \; T$$

$$R \;=\; p \; V \;/\; z \; n \; T$$

$$T \;=\; p \; V \;/\; z \; n \; R$$

Symbol English Metric
$$Z$$ = compressibility factor $$dimensionless$$
$$p$$ = pressure $$lbf\;/\;in^2$$ $$Pa$$
$$V$$ = volume $$ft^3$$ $$m^3$$
$$n$$ = number of moles $$dimensionless$$
$$R$$ = specific gas constant $$lbf-ft\;/\;lbm-R$$  $$J\;/\;kg-K$$
$$\large T$$ = temperature $$F$$ $$K$$

Tags: Gas Ideal Gas