Help Microwave ovens use microwave radiation to heat food. The microwaves are ab
ID: 824211 • Letter: H
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Microwave ovens use microwave radiation to heat food. The microwaves are absorbed by moisture in the food, which is transferred to other components of the food. As the water becomes hotter, so does the food. Suppose that the microwave radiation has a wavelength of 11.2 cm. How many photons are required to heat 200 mL of coffee from 22 degree C to 64 degree C? Express your answer using two significant figures. Suppose the microwave's power is 900W (1Watt = 1Joule/sec). How long would you have to heat the coffee in part A? Express your answer using two significant figures.Explanation / Answer
(A) Mass of coffee = volume x density (assume equal to water = 1.00 g/mL)
= 200 x 1.00 = 200 g
Heat required = mass x specific heat x temperature change of coffee
= 200 x 4.184 x (64 - 22) = 35145.6 J
Wavelength = 11.2 cm = 0.112 m
Energy of 1 photon E = hc/wavelength
= 6.626 x 10^(-34) x 2.998 x 10^8/0.112
= 1.7736 x 10^(-24) J
Number of photons N = heat required/energy of 1 photon
= 35145.6/1.7736 x 10^(-24)
= 2.0 x 10^28 photons
(B) Power = heat required/time
Time t = heat required/power
= 35145.6/900
= 39 s
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