[longemen3000]

We have a solver for the pure critical point, that just finds the (v,T) coordinate that satisfies dP/dV = 0 = d²P/dV². of course, not all EoS can even satisfy this condition. Cubics have the correct temperature and pressure (by definition) but fail on volume. SAFT equations and all EoS with association terms predicts critical points with temperatures higher than the experimental ones. a lot of MultiParameter EoS (like IAWPS95, the standard for pure water) have some anomalies at the vicinity of the critical point. Nevertheless, finding such critical points, however far from reality are from the Real fluid that is trying to represent, helps on finding where are your properties in the phase diagram. In practice, you never stay at the critical point, you pass near it and you can tell by some properties that you are passing near it.

There is also new developments on "Phase equilibria" over the critical point,because it seems that supercritical fluids do present some sort of continuous phase transition between a liquid-like state and a gas-like state. there is this thing named the widom line that marks this separation, But not all EoS even present this line..., "are there phases in the supercritical fluid?" is a research question in that sense.

[bernulli]

I mean something different: no one has ever measured a critical volume, your dp/dv flatlines at the critical point, i.e. there is no driving force to make the fluid balance out the naturally occurring fluctuations, indeed relaxation times go to infinity at the critical point. An EOS only gives you the thermodynamic equilibrium value, attained when you let it sit for times much larger than the relaxation times.

The Widom line(s) are somewhat arbitrarily and ambiguously defined, so I'm not a big fan (pseudo boiling all the way!), but the whole point there is that there is no phase equilibrium at supercritical conditions. However, just because we never observe supercritical liquids and gases simultaneously in equilibrium, does not mean they don't exist. They absolutely do and do lead to a phase transition between liquids and gases - just not coexisting.

This also means that your other comment needs a revision: we absolutely do have something akin to boiling at supercritical conditions, even with macroscopic effects, such as the (subcritical) boiling crisis <> (supercritical) heat transfer deterioration.

[longemen3000]

Of course! we are urgently in need of a "critical boiling" relation. At the moment we are using critical isochores as a way to "extend" the saturation curve, but it is less than ideal (at least they can be calculated quickly).

I agree with the Widom line, at the moment i haven't found any concrete relation to calculate those from a equation of state functional. if there is something concrete, i would be glad to code it.

[bernulli]

That's what I work on, I'll send you an email (if I find your address somewhere)!

[bernulli]

Also - could you explain why you don't count van der Waals' equation among the cubic EOS?