Pizzas in large restaurants are often made in belt furnaces. The pizza is placed on a translating belt that carries it through the oven for a specified length of time. Assume a semicylindrical oven, diameter \(0.75 \mathrm{~m}\), radiating from a hemispherical element like a blackbody at a temperature of \(2000 \mathrm{~K}\). The pizza, \(1 \mathrm{~cm}\) thick, and \(0.45 \mathrm{~m}\) in diameter, is cooked when its centerline temperature reaches at least \(225^{\circ} \mathrm{C}\). If the oven is \(1.5 \mathrm{~m}\) long, how fast must the belt move to insure a correct baking time? You may neglect convection in this analysis. The emissivity of the pizzas may be assumed to be 0.95 and its other thermal properties may be approximated as those of cake batter with a heat capacity of \(2500 \mathrm{~J} / \mathrm{kg} \mathrm{K}\). (You may have to approximate the view factor between the pizza and oven).