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Are EOSs merely correlations that mathematically represent (in a better or worse way) experimental data or do they have a theoretical background? How are they developed (suppose one wishes to develop his/her own EOS -- how would he/she start and which script should he/she follow?).

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  • $\begingroup$ related chemistry.stackexchange.com/questions/549/… $\endgroup$ – Mithoron Jun 3 '16 at 20:02
  • $\begingroup$ At least some EOSes may be derived from first principle using statistical physics approach. However, originally they were developed from general considerations and trial and error. $\endgroup$ – permeakra Jun 4 '16 at 9:33
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They are merely brief and approximated ways to describe observed relations among state parameters. They do not need to have a theoretical background, but many times they have. It helps to create them and provides some reliability. The theory used to guide the construction of a EOS is anyone that turns to be useful.

how would he/she start and which script should he/she follow?

It is a very broad question. In thermodynamics there are few state parameters used normally. Thermodynamic theory is a macroscopic theory of somewhat general applicability, but EOS can be very specific, and this specificity can not be provided by thermodynamics, so, it turns to be a wide search. In cases where simple general relations exist (mostly already discovered), it can be found just by fitting a data to a function.

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  • $\begingroup$ Statistical thermodynamics provides the methodology for deriving the virial equation of state based on first principles. It starts out by looking at the potential energy interactions between a pair of molecules of the gas (to get the first virial coefficient). $\endgroup$ – Chet Miller Jun 4 '16 at 12:08

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