Question

# Suppose that the microwave radiation has a wavelength of 12.4 cm . How many photons are...

Suppose that the microwave radiation has a wavelength of 12.4 cm . How many photons are required to heat 295 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.

first we calculate the change in temperature. T = 62 - 25 T = 37 c = 37 K

the mass of the water is given by
Mass of water = volume of water * density of water
M =295 ml * 0.997 g/mL
M = 294.115 g

the energy needed to change the temperature. is given by :-
Q = T * m * specific heat constant
Q = 37 K * 294.115 g * 4.184 J/(gK)
Q = 45531.3549 J

energy required by a single photon
Energy required by a single photon (photon) = h * c / E(photon) = 6.63x10-34 Js * 3x108 m/s / 0.124 m
E(photon) = 1.604x10-24 J

no of photond required :-

no of photons = total energy / energy of single photon = E / E(photon)
n = 45531.3549 J / 1.604x10-24 J
n = 2.8386 x1028

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