sci.energy

Bill Ward wrote:

> This is an area I seem to have trouble with. I can see two apparently
> equivalent ways to describe the radiation between two bodies:
>
> 1) The way it's actually observed, by measuring the radiation
> transmitted between a hot body and a cold body and their respective
> absolute temperatures. The transferred energy is always found to be from
> hot to cold, proportional to the difference of the 4th power of the
> temperatures.
>
> 2) The mathematical simplification that assumes each is radiating
> isotropically proportional to the 4th power of their absolute
> temperatures, and that radiation is bidirectional between them, with the
> cold object heating the hot object less than the hot object heats the
> cold object. That will give the same result as #1, of course, but
> assumes that the cold object is able to transfer heat to the hot object
> as long as the quantity is less than the energy it receives.
>
> It sounds like a distinction without a difference, until you consider
> the following thought experiment:
>
> Imagine two focal points Fc and Fh, d distance apart. Construct two
> ellipsoidal perfect reflectors around those focii, one skinny(C), of
> minor diameter about d/4, the other fatter(H), of minor diameter about
> d/2 . Now construct a spherical perfect reflector (S) of diameter d
> centered on Fh.
>
> Remove the part of ellipsoid H around Fc outside the intersection with
> sphere S, and similarly the part of ellipsoid C around Fh. Remove S
> except for the annular section between C and H.
>
> What you should have, if I didn't screw up the description too badly, is
> a optical system consisting of a small ellipsoid reflector around Fc, a
> larger ellipsoid reflector around Fh, and an annular spherical reflector
> region centered on Fh connecting the two.
>
> (1) All radiated energy from Fc must reflect to the Fh, since they are
> both foci of the H and C ellipsoids, and Fc can't "see" the sphere S.
>
> (2) But not all of the energy from Fh is reflected to Fc. Fc gets only
> the energy from Fh reflected from the ellipsoids. as the portion
> reflecting from sphere S returns directly to Fh.

I drew this up, and traced the paths at regular angular deflections from
each of the focal points.

I found that there are paths that don't lead directly from Fc to Fh, as
you stated in point (1). Any path from Fc that does not contact first the
small ellipsoid reflector does not lead directly to Fh. So point (1) is
incorrect.

Point (2) has three elements, and you have discussed only two of them.
Paths from Fh a) could reflect off the fatter reflector, then the skinny
reflector, and then to Fc, OR b) from Fh to the spherical reflector
directly back to Fc, and c) the missing case of from Fh to the fatter
reflector to the spherical reflector and then many more reflections.

So both points (1) and (2) in your discussion are incorrect. I'll be
waiting for your corrected discussion. Probably forever.


--
Phil Hays