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Why No Explosion?

Science brain teasers require understanding of the physical or biological world and the laws that govern it.

 

Puzzle ID:#16192
Fun:*** (2.31)
Difficulty:*** (2.34)
Category:Science
Submitted By:Bobbrt*****
Corrected By:MarcM1098

 

 

 



It is scientific fact that if all else is held constant, the pressure of a gas varies directly with its temperature. In other words, if you have a gas in a sealed, insulated, rigid container and you double its temperature, its pressure will also double. If you triple the temperature, the pressure will triple, etc. This is not EXACTLY true, but it is close enough for the purpose of this teaser.

Why is it, then, that if I were to fill my tires with 32 psi of air on a day that is 2 degrees Celsius, the tires won't explode if the temperature later increases to 20 degrees Celsius (which would seemingly increase the pressure 10-fold to 320 psi, well beyond the capacity of most tires)?

Assume that the temperature of the air in the tire always matches the temperature outdoors: it starts at 2 degrees and ends at 20 degrees.
Also ignore the fact that the tires will expand.



Answer

Like the hint implies, the key to this teaser is understanding what you are really doing when you multiply numbers. For example, if you have the number 3 on a number line and you want to double it, what you could do is put your thumb at 0 and your index finger at 3, and then measure off that distance past 3 one time, which will of course bring you to 6. You are essentially doubling the distance that 3 is from 0 to get 6. The only reason this works, however, is because at 0 you really have ZERO length. 0 really means "nothing" in this case. With the Celsius temperature scale, however, 0 degrees does not mean that you have "no temperature". 0 degrees was chosen arbitrarily to coincide with the freezing point of water. Other than that, it has no real significance. So if you want to multiply 2 degrees C by 10, you have to increase its distance from ABSOLUTE zero by 10, not its distance from the arbitrary 0.

Absolute zero is about -273 degrees C. At this point, there really is "no temperature". So when the temperature in the problem goes from 2 degrees to 20 degrees, it is really going a "distance" of 275 degrees from zero to a distance of 293 degrees from zero, which is only an increase of 6.5 percent, not enough to make your tires explode.

The moral of this story is that if you want to multiply numbers, the numbers themselves must represent their "distance" from a true zero. You can add and subtract numbers without knowing this "distance", but you can't multiply and divide.

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