A house with a flat horizontal roof has a black tar waterproof finish. the underside of the roof is well insulated. The upper surface is exposed to ambient air at 297 K. The convection heat transfer coefficient is 10 W/m²K. Calculate the average equilibrium temperature of the roof for the following conditions;
(i) Clear sunny day with incident solar radiation flux of 550W/m² and the ambient sky with an effective temperature of 50 K.
(ii) A clear night with with an ambient sky temperature of 50 K.