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"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.
> >... 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).
> 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 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.
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.