Question

Using your microwave, how many moles of photons are needed to heat up a cup of tea? Consider a cup of tea to be 237mL of water starting at 25.0oC and the drinking temperature to be 85.5oC. Also, most microwave ovens have Klystron tubes tuned to emit microwaves that are absorbed by water molecules at a wavelength of 12.24cm. (enter only your numeric answer, do not include units. Use the format number x 10^number and include 3 significant digits)

Answer 1

Q = m*C*(Tf-Ti)

Q = 237 * 4.184 * (85.5-25)

Q = 59992.284 J

For the wavelength:

E= h c / WL

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

WL = wavelength in meters

E= (6.626*10^-34)(3*10^8)/(12.24*10^-2)

E = 1.6240*10^-24 J/photon

photons = Q/E = (59992.284 ) / (1.6240*10^-24) = 3.6941*10^28 photons

1 mol = 6.022*10^23

x mol = (3.6941*10^28)/( 6.022*10^23) = 61343.40 mol of photons = 6.13*10^4 mol of photons