The M-in-M experiment (Marshmallow in Microwave)

Lab x
Marshmallows, Photons, and Waves

The purpose of this lab is to realize Microwave Oven as a wave-generator producing standing waves, to analyze the characteristics of such wave, and how it generates certain "hot spots" when heating foods.
The second purpose of this lab is to realize that Marshmallow absorbs heat/ energy very easily (swells rapidly within seconds), thus during a nuclear warfare, wearing a marshmallow suit is highly not recommended.
The dimensions of microwaves are L : W : H = (0.36 m : 0.36 m * 0.23 m) +/- 0.001
This blog will answer few questions on a given handout, and they are listed and answered as follows:
1. Determine the frequency of the microwaves
v = λf

length, 12cm +/- 1 (0.12 m +/- 0.0012), is half λ

f = v/λ, whereas v is speed of light (3*10^8)
f = 1.25 GHz +/- 0.0012


2. Deduce the range of possible dimensions including the smallest possible microwaves


The possible dimensions would be the wavelength of the standing wave. It is 12 cm +/- 1. Assuming the microwave is emitting perfectly horizontal wave from side to side, the smallest dimension of microwave therefore is 12 cm by 12 cm by any reasonable height.


- During the experiment, a cup of 100.0 g of water is heated for 30 s, then measured the temperature difference.
Initial temp = 20.0 +/- 0.1 C, final temp = 57.5 +/- 0.1 C. ΔT is 37.5 C. +/- 0.2


3. Total energy content of water?


Energy, or heat, is expressed in Q = m c ΔT. Where c = 4.186 J/g C
Q then, is 100g * 4.186 * 37.5 = 15697.5 J +/- 0.3


*Power, P, is joules per second. The time is 30 s, therefore Power = Q/t = 523.3 W +/- 0.3

4. How many photons per second?
Energy per Photon is expressed in E = h f
frequency is 1.25 GHz +/- 0.0012, while h is planck's constant, which is 6.626068 × 10^-34 m² kg / s


E(per photon) = h f = 6.63 * 10^-34 * 1.25 *10^9 = 8.23 * 10^(-25) J

E(total) = 15697.5 J. +/- 0.0012
# of Photon then, is E(total) / E(per photon) = 1.91*10^28 photons. +/- 0.0012

5. What pressure do these photons exert on the side of the microwaves?

I = P/A
Area of Microwaves is W * L (it's a relatively square microwave) 0.1296 m^2 +/- 0.002
Power is calculated to be 523.3 W +/- 0.3
I = 4037.8 W/m^2 +/- 0.302

p(rad), radial pressure, is I / c;
p = 1.35 * 10^(-5) N/m^2 +/- 0.302

END

Expiration date : 12/ 08/ 2008