A microwave oven heats by radiating food with microwave radiation which is absorbed by the food and converted to heat. Suppose an oven's radiation wavelength is 12.5 cm. A container with 0.250 liter of water was placed in the oven and the temperature of the water rose from 20 degrees celsium to 100 degrees celsium. How many photons of this microwave radiation were required. Assume that all energy from the radiation were used to raise the temperature of the water
E per photon = hc/wavelength
Convert 12.5 cm to m and solve for E.
(note: 12.5 cm = 0.125m)
How much total energy did the water absorb. That's mass H2O x specific heat H2O x (Tfinal-Tinitial).
Eper photon x # photons = total E H2O.
Solve for # photons.
E=mc(T2-T1) =>0.25×4200(100-80)
=8400J
Now,to find N, no of photons
E=Nhc/wavelength => N=E×wavelength) /hc
N=(8400×0.125)/hc
=5.27×10^28
Therefore, the photons were 5.27×10^28
Correct! Just one small error in the calculation, it should be N = (8400 x 0.01) / E per photon, since the wavelength is in meters. But the final answer of 5.27 x 10^28 photons is correct.
To calculate the number of photons of microwave radiation required to raise the temperature of water, we need to consider the energy of each photon and the total energy required to increase the temperature of the water.
First, we can calculate the energy of each photon using the equation:
E = hc / λ
Where:
E is the energy of each photon,
h is Planck's constant (6.62607015×10^-34 J·s),
c is the speed of light (299,792,458 m/s), and
λ is the wavelength of the radiation in meters.
Converting the given wavelength of 12.5 cm (0.125 meters) to meters, we have:
λ = 0.125 m
Substituting the values into the equation, we can calculate the energy of each photon:
E = (6.62607015×10^-34 J·s × 299,792,458 m/s) / (0.125 m)
Next, we need to determine the total energy required to raise the temperature of the water. We can use the equation:
Q = mcΔT
Where:
Q is the energy,
m is the mass of water in kilograms,
c is the specific heat capacity of water (4.186 J/g·°C), and
ΔT is the change in temperature in Kelvin.
Converting the volume of water from 0.250 liters to grams with the assumption that 1 ml of water weighs 1 g, we have:
m = 0.250 kg
Substituting the values into the equation, we can calculate the energy required:
Q = (0.250 kg × 4.186 J/g·°C × (100°C - 20°C))
Finally, dividing the total energy required to raise the water's temperature by the energy of each photon will give us the number of photons required:
Number of photons = Q / E
Substituting the calculated values above, we can determine the number of photons of microwave radiation required to raise the temperature of the water.