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Re: example of alternate form of 1st law



Dadgum it, it turned out to be easier than I expected to come up with
a problem that doesn't lend itself to Q+W=delta(E). Gene Mosca
provided me with it.

Drop a block. The earth does work on the block. But the block does no
work on the earth (because the earth's motion is negligible). Oops!
The resolution of this situation is of course to include the energy
of the gravitational field. But unless one is willing to talk about
work done on a field (and I don't think I am), there's no way to
include this term on the LHS of the 1st law as stated above.

The only way out, I must concede, is to admit that Q+W=delta(E) is
not useful anytime field forces (which are external to the system)
are involved. Unfortunately this includes large numbers of problems.

ps: If you want to try balancing energies in the above problem, I
suggest the following geometry. Take the earth to be spherical and
uniform in density. Instead of a block, consider a shell of mass dm.
Let this shell fall inwards spherically starting from infinity. It
works out nicely: the gain in field energy between the surface of the
earth and infinity equals the loss in potential energy of the mass
shell. You may be more comfortable doing this problem using electric
rather than gravitational fields.

I've been busy with other things the past couple of days, but I see
that I should probably add a few words to this.

Let system A be the block of mass m. To be specific, system A is
everything within the volume of space (both real matter, fields, and
anything else if you think there is anything else) enclosed by the
outer surfaces of the block. (No Klein bottles please!) Let system B
be the rest of the universe.

This time I'll throw the block up in the air from the surface of a
planet. The planet is stationary, extremely heavy and large, and
isolated in deep space. (Add other simplifications if you think it's
useful.)

Let configuration 1 be just after the block leaves my hand with speed
v. Let configuration 2 be the highest point (not very high so we can
assume g is constant) the block reaches.

I trust everyone agrees that E_A1 - E_A2 = mv^2/2. There is no
potential energy term because the planet is not included in system A.
All gravitional self-energy and other rest energy terms of the block
are constants and so don't appear in the difference.

So the block lost energy. According to Q+W=delta(E) this is because
system B did negative work on system A. This is supposed to be
thermodynamically equivalent to saying system A did positive work on
system B, right? Q+W are energy transfers (unlike pseudowork which is
merely a computational device for solving Newton's laws).

Well there's my problem. Clearly negligible work has been done on the
planet. So I seem to be stuck with saying work was done on the
gravitational field in the space between the planet and block (ie. in
system B - as I say, it's much clearer that the changing field is in
the intervening space if the "block" is actually a symmetric shell
around the planet). If we stick with conventional ideas in which W is
the integral of F*ds, I have no idea what this means: ds of what?
Field lines?

So far, I have toyed with 3 possible resolutions of this problem:

1. As mentioned in my original message, concede that Q+W=delta(E)
cannot handle external fields. It only works if you include both
interacting objects and their field in the system. If I understand
some of John Barrer's private messages to me, this is what he would
advocate. But I'm *extremely* unhappy with being forced to choose my
system a certain way. Yes, certain choices may be more practical or
sensible. But, for the record, I flatly reject any version of the
first law or of thermo in general that requires me to choose my
system in only one particular way. (Okay, I'm exaggerating slightly.
QM puts certain constraints on me. For example, artificially drawing
a boundary inside a gas of indistinguishable molecules is not a good
idea. But I want to be free to decide whether to include the piston
or not, for instance.) I am not an engineer who merely wants to be
told "just follow this algorithm and use that formula and then turn
the crank." I am seeking general understanding not recipes.

2. Redefine what Q and/or W means. This is what Gene M referred to:
"W is defined as the energy transfer across a boundary not associated
with a temperature gradient at the boundary. Consequently, not all W
needs to be categorized as Int F dot ds." This is a possibility, but
I'm not sure I'm quite ready to endorse this. I would probably be
happier redefining Q because there's already no end of controversy
over what it means. But I think W = Int F dot ds is pretty firmly
entrenched and I'm reluctant to abandon it.

3. Stealing from the concurrent N#3 thread, invoke gravitons and
somehow talk about doing work on gravitons. I would be glad to hear
from someone more qualified than I to comment on whether "work done
on gravitons" is a meaningful concept and if so what it means.
--
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/