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>> delta E = W + Q
> However, isn't it just fine for reversible processes?
1) To answer the letter (but not the spirit)
of the question, no, just saying "reversible"
isn't enought of a restriction to make the
W+Q law work as a starting point for thermodynamics.
You can if you like define
q := TdS
and
w := PdV
where I am very intentionally writing w and q
in lower case. Both of these critters are
one-forms. They are !!not!! exact one-forms.
There is no zero-form "Q" or "W" such that
q "=" dQ
or w "=" dW
Note the heavy use of scare quotes.
See reference for a picture of a non-exact
one-form.
I intend to duck the issue of whether w or
"W" should be called work, or whether q or
"Q" should be called heat. I prefer to
discuss physics ideas, not terminological
holy war.
Taking stock, we see that we can write
dE = w + q
as an equation among one-forms, but we must
!!not!! write any of the following improper
expressions:
E "=" w + q
E "=" W + Q
E "=" dW + dQ
dE "=" dW + dQ
The creepy thing is that practically everywhere
I look I see improper expressions like that. It
tells me that a lot of people aren't thinking
very clearly about the subject.