sci.energy

On Thu, 23 Aug 2007 20:38:56 -0700, Phil. wrote:

> On Aug 23, 7:03 pm, "daestrom" wrote:
>> "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
>
> In that case you have to use 'view factors' that account for the
> imbalance, texts such as Holman discuss this an example follows:
>
> "Radiation View Factors
>
> The above equations for blackbodies and graybodies assumed that the small
> body could see only the large enclosing body and nothing else. Hence, all
> radiation leaving the small body would reach the large body. For the case
> where two objects can see more than just each other, then one must
> introduce a view factor F and the heat transfer calculations become
> significantly more involved. The view factor F12 is used to parameterize
> the fraction of thermal power leaving object 1 and reaching object 2.
> Likewise, the fraction of thermal power leaving object 2 and reaching
> object 1 is given by F21
> The case of two blackbodies in thermal equilibrium can be used to derive
> the reciprocity relationship for view factors, thus, once one knows F12,
> F21 can be calculated immediately. Radiation view factors can be
> analytically derived for simple geometries and are tabulated in several
> references on heat transfer ( . Holman, 1986). They range from zero
> ( . two small bodies spaced very far apart) to 1 ( . one body is
> enclosed by the other)."
>
> For the equations referred to above see:
> /formulae/heat_transfer/radiation/

That sounds more like engineering. Is there a physical explanation that
goes with it?

My guess is that it has something to do with low energy/temperature
photons not being absorbed by a higher energy/temperature body, due to
filled energy levels. But the necessary QM for that is way over my head.