I think I have finally gotten my head around the idea of
"heat content" aka "thermal energy content". It is /almost/
but not quite always a bad idea. There is one obscure corner
of parameter-space where it actually makes sense.
There are four cases to consider:
1) For an ideal spring by itself, the notion of thermal
energy is unnecessary because there isn't any.
2) For an ideal hot potato by itself, the notion of thermal
energy is unnecessary, because plain old _energy_ suffices.
3) A Slinktato(tm) comprises both a spring and a potato,
but the PdV terms are completely decoupled from the TdS
terms, so that it is impossible to build a heat engine.
In this case we can usefully distinguish thermal energy
content from mechanical energy content. This is an
example of what I call a /compound/ cramped system.
4) For a heat engine, it is mandatory to get rid of the
notion of thermal energy content. Any such notion is
incompatible with understanding what's going on.
I know a lot of people have a knee-jerk response that says
"there's no such thing as thermal-energy content" ... which
is /almost/ but not quite exactly right. Pedagogically,
life would be simpler if we could kill off "thermal energy"
entirely, but that's not going to be possible. As always,
the nastiest misconceptions are the ones that have a grain
of truth to them.
This is new and very drafty. Comments, questions, and
suggestions are welcome.
It will take me some time to rewrite various other documents
to make them consistent with the new and improved way of
looking at things.
Mad props to Jeffrey Schnick for disabusing me of a long-held
misconception and getting me started in the right direction.
I've known for years that something needed fixing.
"I knew it! I knew it! Well, not 'knew it' in the
sense of having the slightest idea, but I knew
there was something I didn't know." http://www.imdb.com/title/tt0533448/quotes