Re: A mind-boggling heat problem through a window

David, 

You have a well thought-out thought experiment started here.  Let's see if I 
can help some.  Recall that the radiant heat is basically infrared radiation 
that is streaming through the window.  It only turns into "usable" heat when 
it hits something and causes it to heat up.  Those objects absorb the energy 
and reradiate as well as heat up the air in contact with the object's 
surface.  Thus, the usable heat in the room DOES change when you add the 
solar panels because they are intercepting the radiation and converting it 
into electricity and clearly some heat.  In the process, it blocks the 
radiation from hitting objects in the room.  However, you also need to 
consider that some of the radiant energy will be reflected back from the 
solar panel and back out the window.  Solar panels tend to be much more 
reflective than, say, a dark couch or carpet and are coated to absorb only 
the wavelengths of radiation that get turned into electricity, reflecting 
away the others.  You could change the angle so that the incoming energy is 
less direct and gets reflected into the room instead of back outside, but 
you will also lower the efficiency of the solar panel because for greatest 
efficiency you want the energy hitting the panel normal (i.e., at 90 deg 
angle) to its surface.  

To figure out the equation, I would look up the information on a typical 
solar panel (efficiency, reflectivity at various wavelengths, etc.) then 
devise a simple room on paper with materials for which you know or can find 
the absorption coefficients.  Then calculate the amount of solar load in the 
room both with and without the solar panel in place.  

By the way, there is no particular reason why a "one way" glass could not be 
used on the solar panel that would keep the heat inside the solar panel, 
except for the fact that the solar panels would probably overheat.  
Depending on the characteristics of the one-way coating, you might be able 
to ventilate the solar panels and use the heat to heat the room.  Of course, 
it might also reduce the efficiency of the panel, as well.  

Good luck
Todd Jamison
Chief Scientist, Observera Inc.