Lab 7: Lab Quiz (3/22/2012) s

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: 12 ± 1cm
• Estimate mass of water: 100 ± 1g
• Change in water temperature: 37 ± 1 ^oC 
• Dimension of Microwave in W*L*H:  (36 ± 1cm) *(36 ± 1cm)*(23 ± 1cm)

Method:

 

Figure 1: Microwave and marshmallow used in this lab.

Analysis:

• 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  

 

Figure 2: Calculation for wavelength, frequency, energy and number of photons.

Table 1: Wavelength and frequency

λ (m)	f (Hz)
0.24 ± 0.01	1.25*109

Table 2: Possible Dimension

Width (m)[ j Є Z+]	Length (m) [ k Є Z+]
0.24 * j	0.24 * k

Table 3: Energy and power.

Total Energy (J)	Power (W)	Energy per proton (J/proton)
15481 ± 200	516 ± 16	(8.29 ± 0.04)*10-25

Table 2: Photon and pressure.

Number of photons (photon)	Pressure (Pa)	Photon per Second (photon/s)
(1.87 ± 0.06)*1028	(1.33 ± 0.048)*10-5	(6.23 ± 0.02)*1026

Conclusion:

In this lab we have discussed the behavior of electromagnetic standing wave through analyzing the physical properties of the microwave. We found that the dimension of the microwave have to include the wavelength of the microwave spectrum. Thus the dimensions of a microwave will always be an integer multiple of the wavelength.