Re: TdS is not dQ or d(anything)

["John S. Denker" <jsd@MONMOUTH.COM>]

On 05/11/2003 09:44 PM, Carl Mungan wrote:
>
> if we restrict ourselves to reversible processes between
> equilibrium states, why do you object to dbar_Q = TdS?

1) I don't know what "dbar" means.  I'll take it
to mean the same as "d" until I hear otherwise.

2) By way of analogy:
Suppose you decide to open a restaurant.  You can
call it _almost_ anything you like ... but if you
try to call it "McDonald's" you're going to get into
trouble.  That name already means something.  It's
already taken.

Returning to thermo:
       T     is well defined
       dS    is well defined
       T dS  is well defined

But that doesn't mean you are free to define dQ
such that
       dQ "=" T dS

The problem is that dQ is not just some heretofore
meaningless name.  It already means something.  It
is equivalent to d(Q) where d is already defined.
You are not free to redefine it.

The problem is not limited to T dS.  The same problems
arise if you try to write:
       d(W) "=" P dV

There is no W such that d(W) "=" P dV (except in
verrrry special cases).

It's like trying to determine the absolute height of
the water in an Escher waterfall.  It just can't be
done.
  http://www.monmouth.com/~jsd/physics/thermo-forms.htm
  http://www.monmouth.com/~jsd/physics/non-conservative.htm

=================

> (I agree that
> this restriction leaves out a lot of interesting physical situations
> however.)

3) Restricting consideration to
>      reversible processes between
>      equilibrium states

is not nearly enough of a restriction to make T dS
or P dV into exact one-forms.  The Carnot engine
reversible and always near equilibrium, but it
does not have any Q-function or W-function such that
       d(Q) "=" T dS
or      d(W) "=" P dV

4) If you do manage to tack on enough restrictions
to arrange that T dS and P dV become exact one-forms,
it leaves out virtually all interesting physical
situations.  It certainly leaves out heat engines.

5) Please don't try to argue that dW is not the
same as d(W).  That would be an abuse of the
terminology.  It would be a tremendous disservice
to students to abuse terminology in such a way.
The subject is hard enough without that.

==============

6)
If you want to talk about T dS, that's fine ... but
you shouldn't call it d(Q) or d(anything).

If you want to talk about P dV, that's fine ... but
you shouldn't call it d(W) or d(anything).

The same goes for any other non-exact one-form.

If you want to integrate a non-exact one-form along
some path, you need to say exactly what the path is.