Question

A typical 760W microwave oven uses radiation with a 12.2cm wavelength.

a) How many moles of photons of this radiation are required to raise the temperature of 405.0g of water from 26.5 to 99.8 Celsius.

b) How long will it take to heat the water?

Answer 1

a)

1) determine the Joules of energy necessary to heat the water:

q = (mass) Δt) (C_p)

q = (405.0 g) (73.3 °C) (4.184 J g^-1 °C^-1)

q = 124208.316 J

2) to determine how many Joules are carried by one photon of wavelength 12.2 cm:

Using λν = c and E = hν,

(12.2 cm) (ν) = 3.00 x 10¹⁰ cm s^-1

ν = 2.459 x 10⁹ s^-1

E = (6.626 x 10^-34 J s) (2.459 x 10⁹ s^-1)

E = 1.629 x 10^-24 J per photon

3) Determination of moles of photons required:

124208.316 J / 1.629 x 10^-24 J per photon = 7.6232 x 10²⁸ photons

7.6232 x 10²⁶ photons / 6.022 x 10²³ photons mol^-1 = 1.266 x 10⁵ moles of photons

b)

1) The microwave delivers energy at the rate of 760.0 J/s.

2) 124208.316 J / 760.0 J/s = 163.4 seconds (a bit more than 2.5 minutes)