Question

Suppose that the microwave radiation has a wavelength of 11.2 cm . How many photons are required to heat 255 mL of coffee from 25.0 ∘C to 62.0 ∘C? Assume that the coffee has the same density, 0.997 g/mL , and specific heat capacity, 4.184 J/(g⋅K) , as water over this temperature range.

Answer 1

E = nhc/λ and Q = mcdT

n= no of photons

λ = wavenlength = 11.2 cm =  11.2 x 10^-2 m

mass of coffee = density x volume = 0.997 g/mL x 255 mL = 254.2 g

dT = 62oC-25oC = 37oC = 37 K

c = specific heat capacity = 4.184 J/(g⋅K)

Therefore,

nhc/λ =  mcdT

n x 6.626x 10^-34 J.s x 3 x10⁸ m/s / 11.2 x 10^-2 m = 254.2 g x 4.184 J/(g⋅K) x 37 K

n =  254.2 g x 4.184 J/(g⋅K) x 37 K x 11.2 x 10^-2 m /  6.626 x 10^-34 J.s x 3 x10⁸ m/s

= 22175 x 10²⁴

Therefore,

no of photons required =  22175 x 10²⁴