Question

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 C 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 C to water at 0 C). 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.

Answer 1

First we have to calculate the volume of the Pizza =

Given volume of the water is 75% of the volume of the pizza. So the volume of the water =     

Density of water = 999.97 kg/m3

mass of water = Volume X density = 551.93656 g

Now to calculate the time taken to heat the pizza to 75 C at low heating

Given only heat transfer from the EM waves to pizza is 80% so at low heating is the power is only 400 W and at hign heating it will be 800 W.

First we calculate the energy required to rise the temperature from -20 C to 75 C. The enrgy required to rise the temp. by 1 C is =

The enrgy required to rise the temp. by 95 C is = 219619.6967482 J

At low heating time taken to rise the temp. by 95 C is seconds or

But Energy required to melt ice at O C to water at O C = 551.93656X334= 184346.81104 J

Tiem required  to melt ice at O C to water at O C = 184346.81104/400= 460 sec. = 7.6 min

So, The total time required to to heat pizza on low setting of the oven to 75 C from -20 C is 9.15+7.6 min= 16.75 min.

In the same way we can calculate time takes to heat the pizza on th high setting of the oven = 4.51+3.072 min.=7.5 min.

The cost of electricity calculated as follows

The cost of one joule energy =

The cost of electricity (for 403965 joule enery) =