Answer:
To calculate the number of photons required to heat the coffee, we can follow these steps:
Calculate the mass of the coffee using its volume and density:
mass = volume x density = 205 mL x 0.997 g/mL = 204.185 g
Calculate the amount of heat required to raise the temperature of the coffee using its mass, specific heat capacity, and temperature change:
q = m x c x ΔT = 204.185 g x 4.184 J/(g⋅K) x (62.0 - 25.0) °C = 32289.6 J
Calculate the energy of each photon using the formula E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the microwave radiation:
E = (6.626 x 10^-34 J⋅s) x (3.00 x 10^8 m/s) / (0.124 m) = 5.067 x 10^-23 J
Calculate the number of photons required to deliver the amount of energy needed to heat the coffee:
number of photons = q / E = 32289.6 J / 5.067 x 10^-23 J = 6.368 x 10^25 photons
Therefore, approximately 6.368 x 10^25 photons are required to heat 205 mL of coffee from 25.0 ∘C to 62.0 ∘C using microwave radiation with a wavelength of 12.4 cm.