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Re: first law of thermo



John Denker wrote:

"Carl E. Mungan" wrote:

F = m dv/dt => F dot dr = m v dot dv

Integrate both sides to get desired result W = delta(K). Add
subscript "com" to W and subscript "TR" to K if you prefer (but you
said this wasn't an argument over nomenclature).

As for terminology, it would be helpful but not
necessary to employ subscripts or some such, for
clarity.

But with or without any particular terminology, the
usefulness of the foregoing calculation is very limited.
-- this W does not represent change in the total kinetic energy
-- this W does not represent change in the thermal energy
-- this W does not represent change in the nonthermal energy.

More generally, I have no idea what this W is good for.
As far as I can tell, it is neither necessary nor sufficient
for deriving and/or explaining thermodynamics. As far as
I can tell, it is a mathematical curiosity which is at best
little more than a waste of time, and more commonly is a
distraction, deflecting attention away from the real,
useful thermo ideas.

O.K. You're entitled not to get excited by solutions of simple
problems, but last week you drew me in to this discussion by claiming
that Carl's solution was wrong. In one message you said it was "not
even close" and in another you said it was off by "roughly a factor
of two." It seems to me that we could have saved a lot of confusion
if you had simply told us that you find it boring!

> >... I've got a pocketful of counterexamples, so
> >any such derivation is going to be quite a rare bird.
>
> Fire away.

The original rotational version of Rumford's experiment
imparts no center-of-mass KE to anything. Yet there
is work (according to the commonsense definition of the
word, which agrees with the technical definition used
by every research physicist I've discussed it with) and
there is production of heat (according to same sort of
definition).

Fine. So now we are back to simple questions of nomenclature as I
thought I understood in the first place. I can deal with that; I
know what you *mean.* But I bristle a bit when people say that
alternate and perfectly correct viewpoints that they simply happen
not to like are "wrong."

> Bulk energy refers purely to translational KE
> of the system's com BECAUSE OF OUR VIEWPOINT. This is zero both
> before and after the interaction, so W-K correctly predicts 0=0.
> Also, there are no external forces on the system, so FLT correctly
> predicts 0=0. This view is thus not very helpful. Let's go on.

The "bulk" property of energy is a red herring.
It has no significance to thermodynamics.
It is a waste of class-time to introduce the concept.
What matters is entropy or the lack thereof.

"What matters" and what is a "waste of time" depends on the situation
and the question. So, again, fine; you don't like it. That doesn't
make it wrong.

... what about viewpoint 3: Suppose I break the system
into two parts, not four:
-- table, and
-- blocks+spring

Then the Work/KE theorem predicts _zero_ which is not
the right answer.

It depends on which work/energy theorem you are talking about. The
one that predicts zero work (or what some of us call pseudowork or CM
work, terms that you have every right to detest if you like) is the
one that is connected to an energy that doesn't change (i.e., bulk or
CM KE.) If you calculate one kind of work and then try to set it
equal to the wrong kind of change in energy you'll probably get the
wrong answer, but the mistake will be 100% yours. If you want to say
there is only one work/energy theorem then you'd better be sure that
you don't go around using different definitions of work or energy.

I don't trust a formalism which produces the right answer
if you know the right answer and produces lots of wrong
answers just as easily.

At least we agree on something!*

John

* The fact is I agree with you on almost all things you write to this
forum and I learn a lot from your contributions. Moreover I
appreciate your wariness of what you call "Proof by Bold Assertion"
and it is largely for that reason that I am surprised when I hear you
saying things that seem so contrary to that philosophy.
--
A. John Mallinckrodt http://www.csupomona.edu/~ajm
Professor of Physics mailto:ajm@csupomona.edu
Physics Department voice:909-869-4054
Cal Poly Pomona fax:909-869-5090
Pomona, CA 91768-4031 office:Building 8, Room 223