The unique relationship between the compressibility factor and the reduced temperature, T _ r, and the reduced pressure, P _ r, was first recognized by Johannes Diderik van der Waals in 1873 and is known as the two-parameter principle of corresponding states.
32.
The quantum gases hydrogen, helium, and neon do not conform to the corresponding-states behavior and the reduced pressure and temperature for those three gases should be redefined in the following manner to improve the accuracy of predicting their compressibility factors when using the generalized graphs:
33.
Figure 2 is an example of a generalized compressibility factor graph derived from hundreds of experimental PVT data points of 10 pure gases, namely methane, ethane, ethylene, propane, n-butane, i-pentane, n-hexane, nitrogen, carbon dioxide and steam.
34.
Where n _ { 3 }'and n _ { 4 }'are the moles of the gas remaining in V _ { t } and V _ { ad } before opening valve C . All of the compressibility factor values are calculated by a proper equation of state, which can generate appropriate z values for temperatures not close to the critical zone.
35.
The compressibility factor at the critical point, which is defined as Z _ c = \ frac { p _ c V _ c } { n _ c k _ B T _ c }, where the subscript c indicates the critical point is predicted to be a constant independent of substance by many equations of state; the Van der Waals equation e . g . predicts a value of 3 / 8 = 0.375.
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