sci.energy

"Phil." wrote in message
news: @ ...
> On Aug 18, 11:58 pm, Bill Ward wrote:
>> On Sat, 18 Aug 2007 18:57:37 -0700, Phil. wrote:
>> > On Aug 18, 6:21 pm, Bill Ward wrote:
>>
>>
>>
>> >> Do you have an explanation for the cavity paradox discussed above?
>>
>> > As I understand your cavity it consists of two partial ellipsoidal
>> > mirrors
>> > facing each other with the F2 of each being the F1 of the other. The
>> > annular gap caused by the different sized ellipsoids is filled by a
>> > partial spherical mirror the centre of which is the focus of the larger
>> > ellipsoid? For simplification we'll assume a vacuum in the cavity and
>> > perfect insulation from outside.
>>
>> > If there is a black body at each focus what is the radiation balance
>> > between them?
>> > Consider any light from the focus of the larger ellipse that doesn't
>> > enter
>> > the second ellipse, it must hit the spherical mirror and be reflected
>> > back
>> > to it's origin, therefore there's no change in heat exchange.
>>
>> Why doesn't that heat count? How does the BB know to ignore it?
>
> It doesn't ignore it, flux leaving the focus and hitting the spherical
> mirror must return to to the focus, therefore fluxin = fluxout and no
> heating.
>

Hi Phil,

But if Fh is radiating at some power (uniformly in all directions) because
it is at some temperature, and Fc is at the same temperature and radiating
at the same power, and all the power radiated from Fc ends up at Fh, but not
all the power radiated from Fh ends up at Fc, it would seem there is a net
power flow from Fc to Fh. And that is the paradox. It would require that
Fh gets hotter (it is absorbing all the radiant energy from Fc but Fc is not
absorbing all the radiant energy from Fh).

Because they are elipsoids with different minor diameters, at one point I
was thinking about the flux densities at different solid angles on the
surfaces of Fc and Fh. For the solid angles of Fh that face S, yes
fluxin==fluxout. For solid angles of Fh facing H (large ellipsoid) or
C(small ellipsoid), it isn't clear that fluxin==fluxout at each angle. The
angles of the ellipsoids mean that the 'fluxin' from the opposite radiant
body changes with angular position to the receiver. So I suspect that a
complete integration through the entire sphere of solid angles surrounding
Fh and Fc would come out to a total energy flow that equals radiant power,
but I haven't the math to prove it.

But just looking at it from the point of all energy radiated from Fc goes to
Fh and not all the energy radiating from Fh goes to Fc implies some sort of
net energy transfer even though we start out with both bodies at the same
temperature. Hence Bill's paradox.

daestrom