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Initially, the distance could be kept constant by placing e.g. a rigid
rod
between the plates which then is removed. But I don't think discussing
such technicalities would be fruitful. In practical terms, the system
is too
clumsy so only the idealized model needs to be discussed. Of course, in
a situation other than an e-mail discussion, I would need more space or
time to define the idealized model so that no confusions could arise.
The curious thing is that, although the model is idealized, it
would
stimulate students to think of both theoretical and experimental
verification
of the second law. The solution (A) predicts that, as the capacitor is
partially immersed (its height with respect to the ground is fixed),
its
"weight" (the net force that pulls it downwards) depends on the
distance
between the plates - the greater the distance, the greater the
"weight". In
contrast, the solution (B) predicts that the "weight" is independent
of the
distance between the plates.
That is what I have been fighting for all along. Not a fanatical
rejection of the second law (which would just be the negative of its
fanatical support) but rather showing ways in which people could reach
clarity for themselves. In the above case, there is an even easier
experimental verification. As the capacitor is half-immersed and water
between the plates has risen above the surface of the pool, one can
punch
a small hole in one of the plates. If water leaks through the hole,
the second
law is violated. I live in difficult conditions and am unable to do any
experiment but a colleague from UCSD did the experiment, hoping to
prove
the validity of the second law in this way. First he informed me that
water did
indeed rise above the surface of the pool, and then he had to punch
the hole
the next day. That was a year ago - so far he has been silent and has
not
replied to my messages.
Pentcho
Ludwik Kowalski wrote:
The vertical plates (before being immersed) attract each
other. A mechanical force, for example from compressed
nylon springs, keeps the distance constant. You say: "We
slowly draw them together (step 1) and so gain some work."
Are you ignoring work that has to be done to further
compress the springs before the immersion?
Ludwik Kowalski
Responding to Brian Whatcott (May 21, 2003) Pentcho Valev wrote:
The source is disconnected before the plates are immersed - I should
have
made this assumption explicit. This suggests another interesting
thought
experiment. The VERTICAL plates are suspended above the pool, ready
for
immersion but the immersion has not started yet. We slowly draw them
together
(step 1) and so gain some work - e.g. one of them, through a pulley,
lifts a
weight. Then we slowly and completely immerse them into the pool
(step
2).
Under water, we slowly draw them apart until the initial distance
between them
is restored (step 3). Since the attraction between them under water
is
much
smaller than the attraction in step 1, the work we spend in step 3 is
much
smaller than the work we gain in step 1. (Since the movements are
very
slow,
friction can be neglected). Finally, in step 4, we slowly withdraw
the
plates
until their initial position is restored.
Now if only steps 1 and 3 are taken into account, the net work
we
gain is
large. The question is: At the expense of what energy is this net
work
(work
gained in step 1 minus work spent in step 3) done? This will answer
your last
question. There are ONLY TWO possibilities. (A) As we immerse the
plates in
step 2 and then withdraw them in step 4, we SPEND net work which, at
the end
of the cycle, appears as net work gained from steps 1 and 3. This
would mean
that the capacitor is "lighter" in step 2 and "heavier" in step 4.
This
possibility is in accordance with the second law. (B) The net work
gained from
steps 1 and 3 is done at the expense of heat absorbed in step 3, as
Panofsky's
pressure pushes the plates apart and absorbs heat in the process.
This
contradicts the second law of course.
Note that, even if (B) is the right answer and the second law is
violated, this by no means suggests that a machine converting heat
into work
under isothermal conditions can be built. Isothermal heat engines,
although
possible in principle (in my view), are extremely slow and
ineffective
and for
that reason it has never occured to serious engineers to try to build
one.
Speculative scientists however have found it advantageous to raise a
postulate
which can be translated like that: "What has not been built and has
not
brought money is impossible". Serious efforts are needed to eradicate
anthropomorphism from physical sciences.
Pentcho