A radiant heating system is installed in the plaster ceiling of a room 18 ft long by 18 ft wide by 8 ft high. The temperature of the concrete floor is maintained at 65°F. Assume that no heat flows through the walls, which are coated with a reradiating material. The temperature of the air passing through the room is held at 65°F. If the required heat supply to the floor is 3,500 Btu/h, calculate the necessary temperature at the ceiling surface. How much heat is transferred to the air, in Btu per hour? Emissivity of plaster is 0.93; absorptivity of concrete is 0.63. The convective heat-transfer coefficient between the ceiling and the air is given by the equation h_c = 0.20(ΔT)^1/4 Btu/ft²·h·°F.