#9 Microwave oven

Objective: 

By the sacrifice of brave marshmallows we shall be able to determine the frequency of the microwave by assuming a standing wave is producing in the oven. Furthermore, a rage of microwave shall be deduced in the dimensions of microwave oven. By heating up water we can acquire the power and then decided how many photons per seconds are oscillating in the microwave and what pressure do these photons exerts.

Data recorded:

      λ= 12 cm, dimension of the oven is 23 x 35 x 35 cm³, mass of water is 100 g, heating time is 30 s, T_i is 20 ℃, T_f is 57 ℃.

Calculation:

       The wave is electromagnetic wave, thus v = c.

       c =  λf , thus f = 3 x 10⁸ / 0.12 = 2.5 x 10⁹ Hz

       C_water = 4.186 J/(g℃)

Thus the energy is E = C_water x m_water x (T_f - T_i) = 15488.2 J

P = E / t = 516.3 W

Energy of photon is E_p = h f = 6.626 x 10^-34 x 2.5 x 10⁹ = 1.65 x 10^-24 J

Thus, total oscillating photon numbers are P / E_p = 3.13 x 10²⁶

Assume power exerts evenly on the inner surface, then

Area = 2 x (0.23 x 0.35 + 0.23 x 0.35 + 0.35 x 0.35) = 0.567 m²

Intensity is I = P / A = 516.3 / 0.567 = 910.6 W/m²

I = P_pressure x c, therefore P_pressure = 910.6 / 3 x 10⁸ = 3.04 x 10⁶ Pa