Suppose that the microwave radiation has a wavelength of 12.4 cm . How many photons are required to heat 255 mL of coffee from 25.0 ∘C to 62.0 ∘C

Explanation:

wavelength λ = 12.4 x 10⁻² m .

energy of one photon = h c / λ

= 6.6 x 10⁻³⁴ x 3 x 10⁸ /  12.4 x 10⁻²

= 1.6 x 10⁻²⁴ J .

Let density of coffee be equal to density of water .

mass of coffee = 255 x 1 = 255 g

heat required to heat up coffee = mass x specific heat x rise in temp

= 255 x 4.18 x ( 62-25 )

= 39438.3 J  .

No of photons required = heat energy required / energy of one photon

= 39438.3 / 1.6 x 10⁻²⁴

= 24649 x 10²⁴

= 24.65 x 10²⁷ .