The black flat roof of a building has an emissivity of 0.9 and an absorptivity of 0.8 for solar radiation. The sun beats down at midday with an intensity of 300 Btu/ft²·h. 

(a) If the temperature of the air and of the surroundings is 68°F, if the wind velocity is negligible, and if no heat penetrates the roof, what is the equilibrium temperature of the roof? For the rate of heat transfer by conduction-convection use q/A = 0.38(ΔT)^1.25, where ΔT is the temperature drop between roof and air in degrees Fahrenheit.

(b) What fraction of the heat from the roof is lost by radiation?