[Phys-L] Re: entropy and electricity

[John Denker <jsd@AV8N.COM>]

Tom Wayburn wrote:

> The question is this:  Is electricity pure work?

No.

> As such is its principle
> characteristic that it carries no entropy?

No.

> (It does not even appear in an
> entropy balance.  See http://tinyurl.com/dyqao.)

That's because you explicitly _assumed_ "electromagnetic effects, etc., are unimportant".

It has long been recognized as a fallacy to assume X and then pretend you have
proved X thereby.  This fallacy even has a name: petitio principii.

> However, packets of
> photons (electromagnetism) carry entropy expressed as s* = S/N = 4.97E-23
> joules per Kelvin, where S is entropy and N is number of photons. [Bowman]
> If so, then why should not electricity suffer from some of the deficiencies
> of electromagnetic waves.

Deficiencies?  Since when is entropy a deficiency?

> After all, electricity behaves like
> electromagnetic waves in a wave guide, does it not?

Waveguides get a little wonky at DC.  I'd recommend using a coaxial cable
rather than a waveguide for your first foray into the thermodynamics of
electromagnetism.

Have you ever heard of Johnson noise?
   http://prola.aps.org/abstract/PR/v32/i1/p97_1
Have you ever heard of Nyquist noise, or the Nyquist formula?
  http://prola.aps.org/abstract/PR/v32/i1/p110_1

More generally:
   http://www.google.com/search?q=johnson+nyquist+1928

Nyquist's argument is a short and sweet, understandable to anyone who has the
slightest understanding of how a coax works, plus the slightest understanding
of thermodynamics.  Consider a cable of length L, treat each standing-wave mode
as a simple harmonic oscillator, write down the thermodynamics for each such
oscillator, and then take the limit as L becomes large.

The brilliantly simple thing is to recognize that an ohm is an ohm is an ohm ...
and a semi-infinite piece of coax is 50 ohms.  That is, a 50-ohm coax (for which
we can readily do the full field theory and thermodynamics, as described above)
must be in thermodynamic equilibrium with an ordinary 50-ohm resistor (which we
can therefore henceforth treat as a two-terminal black box).

Understanding this should be a required part of every physicist's education.  It
is easy, elegant, and useful.  If you've never done the exercise, I recommend
doing it ASAP.

The generalization from coax to waveguide is straightforward, and makes a good
extra-credit exercise.  You will find a generalized version of the Nyquist formula
in which the impedance is a function of frequency ... but otherwise the story is
the same.

The generalization from simple harmonic oscillator to _quantum_ harmonic oscillator
is also quite doable ... and useful.
   http://prola.aps.org/abstract/PRA/v29/i3/p1419_1

> Do wave guides
> annihilate entropy?

You tell me:  Has the second law of thermodynamics been repealed?
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