Re-Inflate a Ping Pong Ball with Proportions
As with all sports, physics determines how things interact. Conversely, sports can explain a lot of the concepts of beginning to intermediate physics. If only high schools taught physics using sports; then, we can have students more engaged and people more aware of their surroundings. Just a thought …
Earlier this week, though, I was reminded of a simple, yet creative way of “re-inflating” a ping pong ball. Simply place the dented ping pong ball in a pot of hot or boiling water and it will magically become spherical again.
Here’s a clip of it in action, from Tricklife.com:
Now, how does it work? Well, we turn to high school chemistry and take a look at the part when we learned about the ideal gas law. That’s pressure times volume equals the number of moles times the gas constant R times the temperature.
Ideal Gas Law
For our purposes, we can simply the idea to proportionality. We get the following three natural laws: Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law. (Actually, these three laws preceded the ideal gas law, which was put together in its entirety afterward.)
Boyle’s Law states that for a fixed mass and fixed temperature, pressure is inversely proportional to volume (that is to say, as pressure goes up, volume goes down, and vice versa). Charles’s Law states that for a fixed mass and fixed pressure, volume is proportional to temperature (as temperature goes up, so does the volume). Finally, Gay-Lussac’s Law states that for a fixed mass and fixed volume, pressure is directly proportional to temperature (as temperature goes up, so does the pressure, for example).
The combination of these three laws gives us the following ratio.
Ideal Gas Proportion
This ping pong ball “trick” can be explained using this proportion. As we increase the temperature by means of hot water, it is required that volume goes up to maintain the constant, which is unknown to us for now (for our purposes, that’s not important, but to be complete, it equals the product of n and R, where n is the number of moles in the system and R is the universal gas constant 0.08205746 L-atm/mol-K). A slight pressure drop will also maintain this constant. Also, we assume that n (a value proportional to the amount of molecules) is constant if we don’t have a puncture in the ping pong ball, a fair assumption, I’d say.
Makes sense, right?
It’s always nice to see chemistry do something practical and useful for us, especially when we have a desk drawer full of supposedly “broken” ping pong balls!
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