Super interesting, and I watched the video on GitHub!
Of course, for an EOS to be useful at the critical point you have to believe that there is such a thing as continuum or even thermodynamic equilibrium at the critical point ;-)
Of course, for an EOS to be useful at the critical point you have to believe that there is such a thing as continuum or even thermodynamic equilibrium at the critical point ;-)
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.
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.
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.