MadSci Network: Physics Query:

### Re: How fast the water molecules move during resonance frequency absorbtion?

Date: Tue Nov 16 11:10:34 2004
Posted By: Jeff Yap, Physics Teacher
Area of science: Physics
ID: 1099762005.Ph
Message:

Hi Arun,

That's a good follow-up question, and it brings up an important concept about temperature. The temperature of something is basically a way for us to measure the speed of the internal molecules. When we heat something in the microwave, we are applying energy to the molecules that makes them move faster and faster.

So, the velocity of the individual water molecules depends on the temperature of the water. The equation breaks down like this:

3/2 k*T = 1/2 m*v^2

T is the temperature in Kelvin,
k is Boltzmann Constant = 1.38066 X 10^-23 J/K
m is the mass of a water molecule = 2.99 X 10^-26 kilograms
(18 grams/mole / 6.02X10^23 molecules/mole)

For water just above freezing, each molecules is moving around 615 meters/second. For water that's almost boiling, each molecules is moving 719 meters per second. These are average speeds.

Wait a second! Does that mean that the molecules in frozen ice are travelling at 615 meters/second? Yup. All molecules of all objects that are NOT at absolute zero are vibrating at some speed. 615 m/s is just the point where the attraction between molecules is enough to keep them together as a solid. 719 m/s is the point where molecular attraction is enough to keep them as a liquid. If the molecules are travelling any faster, they'll fly out of the liquid and become airborne. (also known as boiling!)
The natural frequency of water is a bit more complicated, because it takes into account the mass of water molecules, the attraction between molecules, the distance between molecules, and some other stuff. Suffice it to say that most microwave ovens put out a frequency of 2.5 gigahertz. This means that these microwaves pulse 2,500,000,000 times per second. This isn't the lowest (also known as "primary") resonant frequency for water, but microwave manufacturers use 2.5 GHz because they want the microwave to work at any and all water temperatures. There's lots more techno-babble about resonance, matching, and the engineering of microwaves, but that'll have to be a separate question.

I hope this helps!

Jeff Yap

References:

Kinetic Theory of Gasses
Simple Harmonic Motion
How Stuff Works - Microwaves

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