Re: [Phys-l] heat +- impulse

[John Denker <jsd@av8n.com>]

On 11/05/2007 08:51 PM, LaMontagne, Bob wrote:

> That is exactly why I used that example. 

Yes, the point is well made.

> If you include the heater
> within the boundary that you call a system, then it's traditionally
> called work - if it's considered to be outside the boundary, then it
> is heat. 

And, taking that nice example a half-step farther, we can get 
rid of the water/resistor boundary entirely, and just pass a 
current through the water.  Or we could #&@+ the water in a 
microwave oven.

Yes, according to one sect (but not all), the current doesn't 
"heat" the water, and the microwave oven doesn't "heat" the 
water.  They say it's "work" not "heat".

> I find that to be untenable.

I agree it's pretty high up on the weird-o-meter.  For sure
I'm not going to tell my sister that the microwave doesn't
heat the food.  OTOH I'm not going to argue with the folks who 
hold that view, because it just doesn't matter.  The important 
things are energy and entropy and suchlike, and for these is 
it much easier to find agreed-upon meanings.

>  I totally agree with dropping
> distinctions between dw and dq.

Gaaak!  I wouldn't say that.  I agreed with almost everything
up to that point, but not that, for a couple of reasons.

1) In the case of the aforementioned water-heating schemes, if
you look at the state variables E, S, T, et cetera, there is
a perfectly good description of the macroscopic behavior.  The
effect of the immersion heater and/or the current and/or the 
microwaves is well described by dE = T dS  ... with no P dV 
term observable on any macroscopic timescale or lengthscale.

My point is that if you look at the state variables -- rather
than fixating on some textual definition of "heat" that some
student learned by rote in high school -- then 
  a) there's nothing weird about these water-heating examples, and 
  b) there is a clear-cut distinction between P dV and T dS.

The distinction between T dS and P dV is not always worthwhile,
but sometimes it is.  You can make it particularly worthwhile
by suitable engineering.  Clean limiting cases include
 -- a heat exchanger.  This is essentially all T dS and no P dV.
 -- a thermally-insulated pushrod, gently pushing on a piston.
  This is essentially all P dV and no T dS.

Unclean cases include Rumford's cannon and Joule's paddle-wheel.


2) Secondly, whatever you're doing or not doing, you shouldn't
express it in terms of "dw" or "dq".  
 -- If you mean P dV, say P dV.  
 -- If you mean T dS, say T dS. 
 -- There cannot(*) be any w such that dw = P dV.
 -- There cannot(*) be any q such that dq = T dS.

(*) Except in trivial situations.

There is a newly-coined adjective that I find useful in this
situation:  A vector field is called "grady" if it is the
gradient of something.  For example, dV is grady because it
is the gradient of V.  But P dV cannot(*) be grady.

  Note that students have a strong tendency to assume that
  every vector field is the gradient of some potential.  If
  they're going to believe in (let alone understand) ungrady
  state functions, some effort is required.  Pictures help:
    http://www.av8n.com/physics/thermo-forms.htm#fig-dS-TdS

If we temporarily and hypothetically assume dw means anything
at all, it must be grady, since it is the gradient of w.  But
then it is nonsense to write dw = P dV, since the LHS is grady
but the RHS is not.  So, we have a proof by contradiction:
there is no w that satisfies the equation dw = P dV.

Note that mathematicians use the term "exact one-form" instead
of grady vector.  It means the same thing, but the word "exact"
is seriously misleading to students in this context.

Weird definitions of "heat" and "work" are annoying, but weird
is not the same as provably wrong.  In contrast, dw and dq are 
provably wrong.  I am quite aware that the vast, vast majority
of thermo books are filled with things like dw and dq, but that
doesn't make them any less wrong.

 -- We should expect students to reject equations that have
  dimensions of length on one side and volume on the other side.
 -- We should expect students to reject equations that are
  vector-valued on one side and scalar-valued on the other side.
 -- We should expect students to reject equations that are
   grady on one side and ungrady on the other side.

If you ever feel the urge to write dw=PdV or dq=TdS, lie down 
until the feeling goes away.