The compressibility factor is given by: $$ z=\frac{P\overline{V}}{RT} $$ The Nelson-Obert chart is:


This chart brings the following information:

  1. At very low pressure (Pr << 1), gases behave as an ideal gas regardless of temperature.
  2. At high temperatures (Tr > 2), ideal gas behavior can be assumed with good accuracy.
  3. The deviation of a gas from ideal gas behavior is greatest in the area of the critical point.


$$ T_R=\frac{T}{T_{(At\ critical\ point)}}\\ P_R=\frac{P}{P_{(At\ critical\ point)}} $$

What I don't understand is:

  • Does this chart describe the ideal behavior of a supercritical fluid or a superheated gas or plasma?

Having in mind any phase diagram:

![enter image description here

  • $\begingroup$ In the critical point, Tr=Pr=Vr=1 (under van der waals equation), then Z=3/8=0.375. But the chart shows Z=0.23. The deviation is somehow big, any reason? $\endgroup$
    – John
    Nov 19, 2023 at 12:22

1 Answer 1


It describes the entire region to the right of the vertical dashed line through the critical point.

  • 1
    $\begingroup$ For the values of Pr that they show on the graph, beyond Pr = 1, it is a supercritical fluid. But, there is really no distinction between a supercritical fluid and a superheated gas. $\endgroup$ May 4, 2016 at 4:55
  • 4
    $\begingroup$ Why, it pretty much does. I'd probably add that it does not describe the ideal gas, for there is no such thing as ideal gas. Also, it does not describe the plasma or ionized gas, for the same reason (I mean, they of course do exist in nature, but that's well outside the present chart and the phase diagram). $\endgroup$ May 4, 2016 at 6:19

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