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Suppose we have a $3\cdot 3\cdot 3\,m^3$ room of which one side is glass. And suppose that the other 5 sides have no effect on temperature (super isolation).

We know from physics how to calculate the required amount of energy to heat a specific mass of air. Suppose we calculate that we need X joules to heat the air inside the aforementioned room to some desired temperature.

How does this relate to the actual incoming solar radiation? Radiation in joules per square meters.

My idea would be to multipy the area in direct sunlight with radiation? Or do we need to use the volume in direct sunlight? Or am I just plain wrong in both cases?

  • I hope my assumptions are clear enough.
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Your assumptions are not clear to me. When you say "the other 5 sides have no effect on temperature" I suspect you mean they are perfect insulators. But you have to consider whether they are perfect reflectors too - accounting for all the wavelengths of radiation emitted by the sun and which have not been absorbed by the atmosphere or reflected or absorbed by the glass window. For example whether the 5 walls are painted black or white or are silvered would make a big difference. –  RedGrittyBrick Jun 20 '13 at 15:07

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The amount of energy entering the room is proportional to the area of the window (and the angle of incidence, the characteristics of the glass, etc)

The amount of energy absorbed by the air in the room is proportional to the lit volume of the room

However the radiation entering your room has already passed through a much much much larger volume of air in the atmosphere, so you should expect that much of the sun's radiation that can be absorbed by the air in the room has already been absorbed - so the heating effect may be small.

Most of the heating effect of sunlight in rooms is caused by sunlight heating solid surfaces.

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