Microwave ovens use microwave radiation to heat food. The microwaves are absorbed by moisture in the food, which is transferred to other components of the food. As the water becomes hotter, so does the food. Suppose that the microwave radiation has a wavelength of 11.2 .
How many photons are required to heat 200 of coffee from 24 to 63?
11.2 WHAT?
200 WHAT?
24 to 62 WHAT?
To find out the number of photons required to heat 200 ml of coffee from 24°C to 63°C, we need to calculate the amount of energy required and then convert it into the number of photons.
First, let's calculate the energy required to heat the coffee. The formula to calculate the energy required to heat a substance is:
Q = mcΔT
Where:
Q = energy required (in Joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
Using this formula:
m = 200 g (assuming the density of water is 1 g/cm³, 1 ml = 1 g)
ΔT = (63 - 24) °C = 39 °C (change in temperature)
c = specific heat capacity of water = 4.184 J/g°C (approximately)
Now, let's calculate the energy required:
Q = (200 g) x (4.184 J/g°C) x (39 °C)
Q = 324,672 J
Now, we can calculate the number of photons required to deliver this energy. The energy of a photon can be calculated using the equation:
E = hc/λ
Where:
E = energy of a single photon (in Joules)
h = Planck's constant = 6.626 x 10^-34 J·s
c = speed of light = 3 x 10^8 m/s
λ = wavelength of radiation (in meters)
Converting the given wavelength from cm to meters:
λ = 11.2 cm = 11.2 x 10^-2 m
Now, let's calculate the energy of a single photon:
E = (6.626 x 10^-34 J·s) x (3 x 10^8 m/s) / (11.2 x 10^-2 m)
E ≈ 1.781 x 10^-21 J
Finally, we can calculate the number of photons:
Number of photons = Energy required / Energy of a single photon
Number of photons = 324,672 J / (1.781 x 10^-21 J)
Number of photons ≈ 1.82 x 10^23 photons
Therefore, approximately 1.82 x 10^23 photons are required to heat 200 ml of coffee from 24°C to 63°C using a microwave with a wavelength of 11.2 cm.