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I would like to ask, is there any universal equation of state that holds for any and all classical fluids and gases, derived purely from first principles (though constants in it should be measurable, or derivable)?

The one (class of) equation(-s) that seems to satisfy this requirement is maybe the virial equation, though according to a statement on Wikipedia (which I can not find at the moment) there is no general equation of state.

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  • $\begingroup$ The question here is, to some extent, when is an equation too general to be useful? We can write down the definiton of the equation of state and can probably recaste that in a few ways that are general enough to cover almost any functional form. But the equation you are after is going to have to cover any possible behaviour for a classical fluid, which means it will be so strongly dependent of the properties of a particular material that it may not tell you very much $\endgroup$
    – By Symmetry
    Commented Sep 18 at 10:55
  • $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Commented Sep 18 at 11:36
  • $\begingroup$ Do all fluids and gases behave the same throughout all temperature and pressures? $\endgroup$
    – Kyle Kanos
    Commented Sep 18 at 16:35
  • $\begingroup$ The question is asking about equation in generality as broad as is compressible Navier-Stokes equation, such that the combination of this mysterious equation and Navier-Stokes equation describes any possible (classical) fluid (gas/liquid and their transitions). $\endgroup$
    – luksev
    Commented Sep 25 at 9:21

1 Answer 1

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No such simple equation for macroscopic parameters exist. Van der Waals equation and some of its modifications can be derived from the microscopic theory (e.g., using virial expansion), but they do rather hand-waving job describing gas-liquid transition.

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  • $\begingroup$ But is virial expansion general enough to cover any form of classical liquid/gas and their transitions? $\endgroup$
    – luksev
    Commented Sep 25 at 9:18
  • $\begingroup$ @luksev as the answer says - the van der Waals equation is a rather poor description of phase transitions. Virial expansion is infinite - so it is not clear how many terms is "enough". In general, phase transitions are a rather different beast from the conventional stat. physics, and meaningfully describing them requires different approaches. I recommend Goldenfeld's book: books.google.fr/books/about/… $\endgroup$
    – Roger V.
    Commented Sep 25 at 9:39

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