Question:
A microwave oven is in the back of the class room. We have placed some marshmallows in the microwave to make some measurements of the standing wave. Determine the frequency of this microwave. From this deduce a range of possible dimensions for microwaves including the smallest possible microwave. In this lab we also microwaved a cup of water. What is the total energy content of the captivity? How many photons per second are oscillating in the microwave? What pressure do these photons exert on the side of the microwave?
Data:
Distance between peak energy: 12cm
Estimate mass of water: 100g
Change in water temperature: 37 C
Dimension of Microwave in W*L*H: (36 ± 1cm) *(36 ± 1cm)*(23 ± 1cm)
Method:
The measured distance between peak energy also represents the distance between two adjacent anti-nodes. Thus λ can be calculate by multiplying 2 to the distance.
λ = d * 2
Since the microwave must contain the entire wavelength, the dimension of the microwave must be a positive integer multiple of the wavelength.
width = m * λ, length = n * λ , whereas n and m is positive integer
the smallest dimension would be when n and m equal one
The energy in captivity is in direct relationship with the change of temperature
E = mcΔT
The numbers of proton can be find by dividing the total energy in captivity to the energy a proton holds.
Energy of a proton in microwave: E = hf
c = f λ, f = λ / c
Pressure on the side is directly proportional to Poynting vector and speed of light
P = S / c (assuming the microwave is black body)
S ≈ I, in which I = intensity = power/area
power = E / t
Calculation:
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