What is the difference between an x axis, x plane, and an x contour?
The answer I gave yesterday was true but not especially explanatory.
It's the sort of answer that makes sense if you already mostly know
what's going on, but not otherwise ... which is not exactly good
pedagogy.
That discusses the Carnot cycle, diagramming it several times from
different points of view. There are contours of constant P, constant
V, constant T, and constant S ... which you get to compare.
This stuff is not easy, but it gets a lot easiER if you know the tricks.
After staring at such plots for a few hours you figure out that the
contours are what matters ... not the axes.
This is closely connected to the idea that we have a topology but not
a geometry. As illustrated, you can stretch the diagrams without
changing their meaning.
In case you are wondering how a 240-page screed on thermodynamics could
possibly get by (until recently) without a section on the Carnot efficiency
formula, the answer is simple: I assume there are textbooks in the world.
I don't feel obliged to write up a topic unless I feel I've got something
to say beyond what's already in all the textbooks. Recently I got a flurry
of questions about engine efficiency that could not be answered by reference
to the usual textbook analysis, so I actually had to think about the subject
... and then I wrote up my notes.
That's one nice thing about writing for the web: If I had to sit down and
write a book all at once, that would be no fun at all. However, if I get
to write a little bit every now and then, eventually it adds up.