Photons Required To Heat Coffee In A Microwave Oven

Photons Required To Heat Coffee In A Microwave Oven
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Photons Required To Heat Coffee In A Microwave Oven

Microwave ovens use microwave radiation to heat food. Moisture in the food absorbs microwaves. Food becomes hotter as moisture in food becomes hotter.

How many photons must a microwave radiation with a wavelength of 11.2 cm produce, in order to heat 200 mL of coffee in a microwave oven, from 23^o C to 60^o C?

The strings:

S₇P₃A₃₂ (Force - Push).

The math:
Pj Problem of Interest is of type force (push). Energy is the capacity to do work which is actualize by force. Light energy can do a pull or push work. The push work is more common. In this problems the photons are being pushed out. Hence the Pj Problem of Interest here is of type force-push.

Photons Required To Heat Coffee In A Microwave Oven

Energy in one photon = E = hν-----------(1).
Where E is the energy of one photon; h is Planck's constant (0.66252 x 10^-33 Js) and ν is the frequency of the microwave.
ν = (velocity of light)/(wavelength of light)
= (3 x 10⁸)/(11.2 x 10^-2) = 26.79 x 10⁸ Hz Hertz cycles per second).
So, Energy of one photon of microwave with wavelength 11.2 cm is:
= hν = (0.66252 x 10^-33)(26.79 x 10⁸) = 17.75 x 10^-25 J.

Specific heat of water = 4.184 J.
Density of water = 1gm/mL
Assuming coffee is dilute aqueous solution
So, specific heat of coffee = specific heat of water.
So, Energy required to heat 200 mL of coffee from 23^o C to 60^o C
= 4.184 x 200 x (60 -23) = 4.184 x 200 x 37 = 30.961 x 10³.

So, number of photons required to heat coffee in the microwave oven from 23^o to 60^o when the wavelength of the microwave radiation is 11.2 cm is:
(30.961 x 10³)/(17.75 x 10^-25) = 1.7 x 10²⁸

Math

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