Application: Heating Food in a Microwave Oven. A frozen pizza is marketed to be heated in a microwave oven. As an engineer you are asked to write heating instructions, specifically how long should it be heated to reach a proper temperature. The average residential microwave oven is 50 cm wide, 40 cm deep, and 30 cm high. The oven has a low and a high heating level. At low, it produces a time averaged power of 500 W, whereas at high, the power is 1000 W.
We will assume the pizza is placed flat on the bottom of the oven and any power coupled into the pizza enters from above. The pizza is 25 cm in diameter, 1.5 cm thick, and is 75 % water by volume. The microwave oven heats the water in the pizza. The frozen pizza is at 20 oC and must be heated to 75 C. Heat capacity of water is 4.1885 J/ (gK) and the latent heat (of melting ice) is 334 J/g (heat capacity is the energy needed to raise the temperature of one gram of substance (water in this case) by 1 degree Kelvin, and latent heat is the energy required to melt a gram of ice at 0 oC to water at 0 oC). Assume that the heat transfer from the electromagnetic waves to the pizza is 80 % efficient and calculate:
(a) The time it takes to heat the pizza on the low setting of the oven.
(b) The time it takes to heat the pizza on the high setting of the oven.
(c) The cost in electricity to heat the pizza if a kW h costs $0.16.