Synonyms: Compressibility factor = Z-factor

Dimensionless multiplier in real gas equation of state which describes the deviation of a real gas from ideal gas behavior:

(1)	$\begin{array}{l}\displaystyle Z = \frac{p V}{\nu R T}\end{array}$

where

$\begin{array}{l}p\end{array}$	$\begin{array}{l}V\end{array}$	$\begin{array}{l}T\end{array}$	$\begin{array}{l}R\end{array}$	$\begin{array}{l}\nu\end{array}$
fluid pressure	fluid volume	fluid temperature	gas constant	Amount of substance

It is related to gas compressibility $\begin{array}{l}c_g\end{array}$ as:

(2)	$\begin{array}{l}\displaystyle c_g(p) = \frac{1}{p} - \frac{1}{Z} \frac{dZ}{dp}\end{array}$

(3)	$\begin{array}{l}\displaystyle Z(p) = \frac{Z_0}{p_0} \cdot p \cdot \exp \left[ - \int_{p_0}^p c(p) dp \right]\end{array}$

Derivation

(4)	$\begin{array}{l}\displaystyle c_g = - \frac{1}{V} \frac{dV}{dp} = - \frac{d}{dp} \left( \ln V \right) \rightarrow \ln \frac{V}{V_0} = - \int_{p_0}^p c(p) dp\end{array}$

Substituting $\begin{array}{l}V\end{array}$ from (1) into (4) one arrives to (2).

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