melting butter in a microwave

["Carl E. Mungan" <cmungan@UWF.EDU>]

I would like to hear more thoughts about John Denker's question:

> Suppose I shine a high-power microwave beam
> onto a chunk of butter.  I think it heats the butter.  Does anybody really
> think this should be described as work not heat?

Dan Schroeder and John Mallinckrodt both said "yes." But I ask: what is the
general framework for dividing radiation into heat vs. work?

At one extreme, we have blackbody radiation which we would probably all
call heat. At the other extreme, we have (ideal) monochromatic laser
radiation which should perhaps be called work because this beam has zero
radiation entropy. If you'll allow the colloquialism, this beam is
"perfectly ordered." Radiation entropy is defined in statistical mechanics
by considering photon mode occupation numbers and is thus related to the
bandwidth, coherence, and directionality of the beam.

So if we look at a real microwave beam, it would seem to me it carries some
rates of entropy S_dot and energy E_dot, but its temperature T is *not*
E_dot/S_dot in general. So perhaps melting butter in a microwave is a
process that *cannot* be neatly divided into either work or heat, but is
rather mostly work and some heat. The opposite would be true if its
bandwidth approached a Planckian distribution and it were fully incoherent
and isotropic. Carl

ps: On the topic of female contributors and the question of civility in the
recent "arguments," perhaps I might be allowed to post an old exchange from
the list:

-----

Date: Fri, 12 Sep 1997 07:45:02 -0700
From: Leigh Palmer
Subject: Style

Ludwik Kowalski says:

> In my opinion "public snipings" and "embarassing comments" are
> perfectly OK as long as we know that everybody is motivated by the
> concerns which unite us on this list. We learn from each other and
> this is the most important.

Hear, hear! This is academic debate. Our style may not be correct
"netiquette", but many of us are utterly fed up with artificial
correctness. I'll join your party, Ludwik.

Leigh

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Just as we want our students to stick their necks out and ask "dumb
questions" in class, let's try to encourage that on the list too. I, for
one, am willing to stand and be counted among the dummies!

Dr. Carl E. Mungan, Assistant Professor     http://www.uwf.edu/~cmungan/
Dept. of Physics, University of West Florida, Pensacola, FL   32514-5751
office: 850-474-2645 (secretary -2267, FAX -3323) email: cmungan@uwf.edu