### Brain Teasers

# Why No Explosion?

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.

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.

### Hint

This problem is really more mathematical than scientific. Here's a hint: say you have a temperature of -10 degrees Celsius. Now double that temperature. You get -20 degrees. Doesn't it seem a little odd that when you double something's temperature that it actually goes DOWN?? When you double something's LENGTH, it never goes DOWN. What's wrong here?### 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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## Comments

I enjoyed this teaser because it taught me why something that I have observed to be true is true. It is always nice to be able to explain something, such as why the sky changes colors. I can't wait until my little one is old enough to ask me that one. Of course, I might have to e-mail bobbrt from time to time when the questions get tougher!

nice one tough one but a good teaser.

If the initial temperature was 0 Celsius and it increased to 20 Celsius it represents an infinite increase and your tyres could cause the whole universe to explode. This is why I always check my tyres only on hot days.

But then if you overinflate your tyres like I did on my caravan, that small % increase (also caused by friction as well as the air temperature) can be enough to explode the tyres.

The teaser took me a while. My physics isn't what it used to be.

The teaser took me a while. My physics isn't what it used to be.

rather complicated.

it could also be that the tires were not outside in the temp change, but rather inside or sheltered, and kept at a regulated room temp, keeping the pressure from changing due to the fact there would be virtually no effect from the change in temp outdoors.

there is a scale for which the temperature can be used to multiply. It is called the Kelvin scale and it starts at 0K (no degree symbol) and that is absolute zero. the unit is just as big as a degree celcius.

I was figuring that the air outside the tires would be increasing pressure at the same rate, so they would stay in check with eachother. I guess, though, that the nearly infinite space of the atmosphere would make it very difficult for atmospheric pressure to change too much....anybody care to explain wany points I'm missing?

It was Interesting it taught me alot

Speedy, you pretty much answered your own question. A change in the temperature of atmospheric air won't change its pressure much at all, because there's so much room for it to expand.

yeah you have to use kalvins in order to solve this one. the formula is 273 + xC

Actually, this isn't really physics, it's chemistry.

Yay for me actually paying attention in chem!

Really easy if you know it, really tough if you don't ;-)

Yay for me actually paying attention in chem!

Really easy if you know it, really tough if you don't ;-)

great teaser, if i hadnt taken and done so well in ap physics this year, i would have had no idea that it truly mattered switching into kelvins

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