Instant Notes: 2. PVT Behavior
Generalized Compressibility Factor Correlations

van der Waals generalized the \(PVT\) behavior based on \(T_c\), and \(P_c\), as \[Z = f(T_r,P_r) \tag*{(9)}\] where \(T_r = T/T_c\) = reduced temperature, and \(P_r = P/P_c\) = reduced pressure.
The above equation form is called as twoparameter corresponding state principle. According to this equation, at a given reduced pressure and reduced temperature all components has the same \(Z\).

To improve the accuracy of property predictions, Pitzer and coworkers introduced the acentric factor \(\omega\) as a third correlating parameter. \[Z = Z^0(T_r,P_r) + \omega Z^1(T_r,P_r) \tag*{(10)}\]

The acentric factor (\(\omega\)) was developed as a measure of the difference in structure between the material of interest and a spherically symmetric molecule such as argon.
The parameter (\(\omega\)) is defined using the reduced vapor pressure as \[\omega = \log_{10} P^{\text{sat}}_r_{(T_r=0.7)}  1\]
The acentric factor reflects the geometry and polarity of a molecule. It is essentially zero for the simple fluids Ar, Kr and Xe. For other fluids, \(\omega\) lie between 0 and 0.4.