Question

Microwave ovens heat food by creating microwave electromagnetic radiation that is absorbed by water molecules in the food. Any material that does not have water in it will not absorb the radiation and will not get hot. Metals reflect the microwaves from their surfaces and disrupt the operation of the oven. Some Australians heat water in microwave ovens to make tea. What is the minimum number of microwave photons with a wavelength of 3.17 mm that will have to be absorbed by a 119.00 gram sample of water to heat it from 25°C to 100°C? (It requires about 315 joules of energy to heat 1 gram of water 75°C)

Answer 1

heat required to heat 119g of water

q = msdT

q = 119 * 315 (for 75 C heat requires for 1 g is 315 J given)

q= 37485 J

Now microwave wavelength = 3.17 mm

so energy = E= hc/lambda

h = 6.6*10^-34 c = 3*10^8

lambda = 3.17 mm = 3.17 * 10^-3 m

putting all these values

E = (6.6*10^-34 *3*10^8) / 3.17 * 10^-3

E = 6.24 * 10^-23 J

number of photons = 37485 J / 6.24 * 10^-23 J = 6*10^26