Question

suppose that the microwave radiation has a wavelength of 11.6 cm . How many photons are required to heat 245 ml of coffee from 25.0 °C to 62°C? Assume that the coffee has the same density 0.997 g/mL and specific heat capacity of 4.184 J/ (g•K), as water over this temperature range.

Answer 1

First part: Find energy required to heat water

E = m Cp dT

E = energy to heat coffee

m = mass coffee = 245 mL x (0.997 g / mL) = 244 g

Cp = heat capacity of coffee = 4.184 J / g K

dT = change in temp of coffee = (62.0 - 25.0) ^oC = 37.0 ^oC

E = (244 g) x (4.184 J / g K) x (37.0 ^oC) = 3.78 x 10⁴ J

Second part: Find energy of a single photon of the radiation

E = ħc / λ

E = energy of the photon

ħ = plancks constant = 6.626 x 10^-34 J s

c = speed of light = 3.00 x 10⁸ m/s

λ = wavelength = 11.6 cm = 11.6 cm x (1m / 100 cm) = 0.116 m

E = (6.626 x 10^-34 J s) x (3.00 x 10⁸ m/s) / (0.116 m) = 1.71 x 10^-24 J

Finally

3.78x10⁴ J x ( 1 photon / 1.71 x 10^-24 J) = 2.21 x 10²⁸ photons