The ceiling of an auditorium consists of a 20 cm thick concrete slab with a thermal conductivity of 1.5 W/m C and with an area of 800m2. At noon a solar radiation of 850 W/m2 is received. The emissivity of concrete is 0.9 and its solar absorbance is 0.6. The roof loses heat by convection to the ambient at 20C with a convection coefficient of 7W/m2 C, and towards the sky for radiation that has an equivalent sky temperature of 2C. If the temperature of the exterior surface of the concrete slab is 50C, determine (a) the heat transfer (Watts) into the building and (b) the temperature of the interior surface of the concrete slab.