Question

Using Microwave Radiation to Heat Coffee (expanded) Microwave ovens use microwave radiation to heat food. The microwaves are absorbed by the water molecules in the food, which is transferred to other components of the food. As the water becomes hotter, so does the food. Part A Suppose that the microwave radiation has a wavelength of 12.4 cm . How many photons are required to heat 215 mL of coffee from 25.0 ∘C to 64.6 ∘C? The coffee has a density of 0.997 g/mL , and a specific heat capacity of 4.179 J/(g⋅K) over this temperature range. Express the number of photons numerically (use scientific notation). 2.19•1020 photons SubmitHintsMy AnswersGive UpReview Part Incorrect; One attempt remaining; Try Again

Answer 1

Q = mcdT

m = volume x density = 215 mL x 0.997 g/mL = 214.355 g

c = 4.179 J/(g⋅K)

dT = 64.6 ∘C - 25.0 ∘C = 39.6 oC = 39.6 K

Q = mcdT

    = 214.355 g x 4.179 J/(g⋅K) x 39.6 K

   = 35473 J

Q = 35473 J

Therefore, enerhy of photons required = 35473 J

  E = nhc / λ    n = no of photons

Given that λ = 12.4 cm = 0.124 m

Then,

35473 J = n x (6.626 x 10^-34 J.s) (3 x 10⁸ m/s) / (0.124 m)

n = 221.3 x 10²⁶ photons

Therefore,

221.3 x 10²⁶ photons are required to heat 215 mL of coffee from 25.0 ∘C to 64.6 ∘C.