A passive solar home in Iowa has 40 M^2 of south-facing double-pane windows and 100 metric tons (100,000 kg) of concrete heat storage. It has a backup furnace whose heat output is 40 MJ/h. Concrete has a heat capacity of about 800 J/C KG (about one-fifth that of water). Suppose that on a sunny winter day each square meter of windows admits 16 MJ of solar energy into the home.
(a) How many hours would the furnace have to run to provide the home with the same amount of heat as was admitted by the windows?
(b) How much would the thermal storage warm up if 40% of the solar heat were lost through the windows, walls, and roof of the house and the other 60% went to heat the storage?