Two boxes are designed to collect solar heat. Each box is of identical
size and shape (aprox, 4' x 8' x 3.5") and each box has an identical
glass cover on the top to let light in.  Rigidity is not a concern;
therefore the sides and back are constructed of a 4' x 8' foam
insulating material that can be purchased at most mega
home-improvement centers.

The one difference between the two boxes is one box has a sheet of
galvanized metal adhered to the inside bottom. After both boxes are
constructed each box has all interior surfaced painted flat black on
the inside (prior to affixing the glass). All visible surfaces on the
inside of each box is painted flat black.

Which box gets hotter, the box with the metal or the box without the metal?

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Clarification of Question by johnjri1-ga on 06 Nov 2006 08:03 PST

Hi, I was thinking about my question and realized a certain aspect of
it may have been vague. When I asked 'which box gets hotter?', I was
refering to the air temperature inside the box (that's its purpose, to
heat air that flows through). I'm not interested in the surface
temperature of the box itself.

Thanks for all the great comments!

In my opinion, they would be both be the same temperature, assuming
that the foam and the metal were equally smooth.

Would not the metal plate take a bit more energy to heat up ?

One box is effectively heating air, the other is heating air and a lump of metal.

Well frde

    That depends if we are thinking about a transient or steady state situation.
Question does not say. It is natural to assume as default steady state, in which
the thermal capacity and intertia is irrelevant.

I wonder what is a purpose of such a question.

There are groups who study forms of solar cooking with the hope of
helping people in Africa.  Parabolic reflectors are good, and seen in
Tibet, but I read that they aren't the answer for the traditional
cooking mehtods of other folks.
I expect that the subject has been fairly well covered.  What I read
was in a German article about a project that was receiving DM 3
million funding.

There should be information on the web, but for two dollars, finding a
specific answer to this question might be too much work.

@Hedgie

From the insulating foam and glass top I inferred that the 'box' was a
closed environment.

Hence two identical boxes, but one contains an ice cube.

Personally I would prefer to use the box with the galvanized base as
it would act as a heat reservoir.  Also I guess this is some sort of
solar still, but it could be a convective oven ...

As for as I know, the air temperature should be the same, as well.

From the physical point of view the key to this answer it the type of
glass that is used to cover the box.

Black paint on the bottom of the box is used to absorb the solar
radiation effectively. At this point the "black" means that it absorbs
optical radiation: the light visible by human eye. However, solar
radiation carries energy in its non-optical spectrum as well. These
include infrared and ultraviolet radiation.
According to the Plank's theory photons with higher frequencies carry
more energy. Hence in your application ultraviolet part of the solar
radiation is the one that may make difference.

Interestingly, it is the higher frequency radiation that can penetrate
deeper into the surfaces (painted layer in your case). In this case
the underlying material will cause a difference. Metals are very good
in both, absorbing high frequency radiation as well as conducting heat
compared to other materials (foam insulator?).

Hence, the metallic bottom CAN provide notably more absorbtion.
And the key now is the glass cover of the box. It is transparent for
the light visible by human eye - that is why we call it "transparent".
But how does it interact with higher frequency solar radiation that
carries significant amount of solar energy?

There is a recipe for the best performance: use the Quartz class. They
are transparent even at higher frequencies.

A regular glass does not have such property - they are characterized
by increased absorbtion. This means that not all ultraviolet light
will reach the bottom of the box to be consequently absorbed by the
metal plate.
However, it is highly probable that some radiation will still make
through - especially at frequencies close to the high end of the
visual spectrum.
In this case, the metal bottom should bemore effective in heating the
air passing through the box.


Search following keywords for more insight:

Optical Calorimetry

What about the fact that the plate will reflect some light back out?

If your black paint is really good at absorbing the entire spectrum
then i would think the all black box would heat up faster but to the
same temprature as the other box if it's a closed box.

If air is flowing through the boxes and the black paint is as good an
absorber as the metal I think the non metal box would be better at
heating the air just because the plate will reflect SOME energy in the
form of visible light.

Of course the metal will probably hold a lot more heat so if you let
the boxes heat up to full temprature THEN start piping air through
them the box with the mteal will stay hotter longer...

I think... :-)

@egon_spangler-ga 

It seems the galvanized metal plate will also be painted black.

I reckon that the one with the metal plate will take longer to heat
up, and you illustrated that neatly when you said that the box with
the metal will stay hot longer.