Re: [Phys-l] T dS versus dQ

[John Denker <jsd@av8n.com>]

On 01/11/2010 01:53 PM, Carl Mungan wrote:

> I know we've been over this before 

Yes, we have been over it before.  I learned some
important things from the discussion.  Thanks!

> and you have addressed it in your 
> own writing. 

Yes, I have opinions on the matter.  But you guys
have on various occasions convinced me that I didn't
understand things nearly as well as I thought I did,
so I'm still listening and still asking bona-fide
non-rhetorical questions.

> But I think part of the rationale for heat/work 
> divisions is simply an attempt to categorize how the energy is 
> initially input (as opposed to how it eventually becomes distributed 
> over the internal modes). It might be a weak rationale but there it 
> is. 

By way of background:  I think we all agree that
under mild assumptions we can write

     dE = T dS - P dV

and if somebody wants to say that the RHS consists
of a "heat" term plus a "work" term then I don't 
have much of a problem with that.  It's *one* of 
the things that people commonly mean by heat and
work.  It's one aspect of the chimera.

So far so good.

But I think I want to ask a much narrower question.

I'm wondering if it is possible to construct a
scenario along the following lines:  In some
context, your student or your colleague writes
"T dS" and then you say no, that's not right, 
you have to write "dQ" here.  Then the other
guy asks what about "dE" and you say no, that's
not right either; you have to write "dQ".

So that's the question:  Is there any scenario in
which it is not OK to replace dQ by either dE or
T dS?  If so, what is the scenario, and why is 
dQ irreplaceable?  Operationally, how do I measure
dQ in this scenario, and/or how do I calculate it?

I conjecture that no such scenario exists.  I've
checked quite a few cases, and so far dQ has always
been easy to replace.  If there is some scenario
I have overlooked, I'd like to hear about it.