Re: W+Q deprecated

["Carl E. Mungan" <mungan@USNA.EDU>]

John Denker wrote:

>  >>     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.

Can you give me an example or two of a reversible process for which
this division into W and Q fails?

Or to put the question another way, is there a problem with the
standard formula dS = dQ_rev/T which implicitly assumes that Q_rev is
the same for any reversible path connecting the initial and final
states of the system (assumed to be equilibrium states)?

> You can if you like define
>         q := TdS

I'm only happy with this for a reversible process. In the canonical
example of a free expansion of an ideal gas, both q and w are zero
and yet S changes. So instead we perform a quasistatic expansion
against a piston and then a quasistatic electrical heating, with the
latter equating to TdS.

(Yes I know we've been over some of this before, but I also maintain
a tight grip on old ideas until the support for a contrary view
becomes convincing enough.)

> 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.

I agree this is a problem. I take it you're not fond of "inexact
differential" notation, ie. my use of dQ_rev above could be written
"d_bar Q_rev" to emphasize the point that Q is not a function and so
dQ does not mean a derivative but just a small amount. Clumsy indeed
and I note Bauman is one example of a thermo text that instead uses
small q and big Q to denote an infinitesmally small and a
non-infinitesmal (sometimes misleadingly called "finite") amount of
energy transferred thermally, respectively. Carl
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/