Re: Non-conservative forces in a liquid dielectric

[Pentcho Valev <pvalev@BAS.BG>]

Brian Whatcott wrote:

> At 05:48 PM 5/20/2003 +0300, Pentcho,  you wrote:
> > /snip/
> > water comes between the plates and even rises high above the surface of
> > the pool. At
> > the expense of what energy? Again, a freshman who has studied the first
> > law may ask
> > you this simple question.
> >
> > Pentcho
>
> I will offer a freshman's naive response as a straw-man:
> the energy needed to raise water above the surrounding surface would be
> supplied by
> a current pulse into the charged capacitor?
> If water is added after the current source is disconnected, then a portion
> of the
>   stored energy is taken?

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