One of the biggest peeves I have regarding the teaching of
thermodynamics is that I was left with a terrible misconception
when I got my AB in physics. I believed that the van der Waals
equation of state was a good model for real pure substances. It
isn't even close for any particular pure substance!
This conceptual butchery was carried even farther (reinforced)
by the introduction of the "Maxwell construction" which yields
a plausibility argument for phase metastability in superheating
of liquids or supercooling of vapors.
Was I the only person taken in? I'm sure glad I wasn't still
suffering from that misconception when I finally taught my own
first group of thermodynamics students. I still used the model,
but I told them it was wildly nonrepresentative of reality. The
only reason for introducing it, so far as I can tell, is that
the "answers" (e.g. critical point, etc.) come out in closed
mathematical form in terms of the vdW coefficients.
Now we all have marvelous numerical engines which, if they must,
can take second derivatives of numerical sequences and such. Is
there an introductory text which takes a numerical approach to
classical themodynamics?