An opaque, diffuse, gray (200mm x 200mm) plate with an emissivity of 0.8 is placed over the opening of a furnace and is known to be at 400K at a certain instant. The bottom of the furnace, having the same dimensions as the plate, is black and operates at 1000K. The sidewalls of the furnace are well-insulated. The top of the plate is exposed to ambient air with a convection coefficient of 25W/m^2?K and to large surroundings. The air and surroundings are each at 300K. If the plate has mass and specific heat of 2kg and 900J/kg.K, respectively, what will be the change in temperature of the plate with time, dTp/dt? Assume convection to the bottom surface of the plate to be negligible. Evaluate the net radiative heat transfer to the bottom surface of the plate