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Path: utzoo!watmath!clyde!cbosgd!cbdkc1!desoto!packard!topaz!josh
From: josh@topaz.ARPA (J Storrs Hall)
Newsgroups: net.physics
Subject: Re: TPMMTP (Thermodynamic PMM to ponder)
Message-ID: <1761@topaz.ARPA>
Date: Wed, 24-Apr-85 17:46:53 EST
Article-I.D.: topaz.1761
Posted: Wed Apr 24 17:46:53 1985
Date-Received: Thu, 25-Apr-85 04:38:17 EST
References: <517@terak.UUCP>
Reply-To: josh@topaz.UUCP (J Storrs Hall)
Organization: Rutgers Univ., New Brunswick, N.J.
Lines: 41

In article <517@terak.UUCP> dennis@terak.UUCP (Dennis Kodimer) writes:
>***
>...
>
>Construct a vessel of two ellipsoids with different diameters and
>common focal points.  Combine half of each ellipsoid with a spherical
>surface which has one of the focii as a center.  
> [all the radiation from f1 is]
>sent to f2.  However, not all radiation from focus f2 is focused onto
>f1; the fraction which meets the spherical surface is returned to f2.
>
>So, as time goes by (another assumption, albeit a persistent one), the
>bulb at focus f2 will receive more radiation than the bulb at focus f1.
>			  /    / \
>Dennis Kodimer		 /    /still waiting for the
>			*----* electrician or someone

Very ingenious!  Here's an even simpler version:  an ellipsoidal
reflector, with a large bulb at one focus and a small one at the other.
For the total radiation flux each way to be the same, the small one 
has to be hotter.  Now construct an ordinary heat engine between them.

Now, if I understand thermodynamics as well as I think (not that that's
very well), the bulbs in either case will be the same temperature,
and the total radiation from one to the other will be the same both 
ways.  Each bulb will "see" the other bulb, or part of itself, in all
directions, and this reflected bulb surface will all be the same temperature.
In the different sized bulb case, the dilemma is easily solved
by geometry--part of the bigger bulb will be farther off-focus than
any of the smaller, so some of its radiations miss the smaller bulb
and rebound to it.  This makes the problem equivalent to two equal-
sized bulbs in an ellipse and another (arbitrary-sized) one in a sphere.

I believe the geometry geometry in Dennis' problem works out the
same way, though I haven't proved it.  The trick is that one of the
foci is close to the "tight" reflector and far from the broad one,
and the reverse for the other focus.  I conjecture that this means
that for bulbs of equal size in Dennis' gadget, much of the radiation 
from f1 would miss f2 and hit f1, solving the mystery.

--JoSH