Steady-state temperature and relfectivity using thermal radiation. Solution in JPG format.

Consider venetian blinds that are painted black on one side and white on the other. Assume that the blinds are installed between two panes of glass, with a vacuum inbetween so that air and its convection have no effect on the problem. Assume that the reflectivity of the white side is 90% and that of the black side is 10%. How well does it work to turn the white side of the blinds outward when the room is already hot to reflect heat, while turning the black side outward to absorb heat when the room is too cold? Assume that the radiation from outside is 1 kW/m2. Find the steady-state temperatures due to just thermal radiation (Stefan-Boltzmann law).