### Brain Teasers

# Double the Pressure

In general, if you have a gas in a container and you double the amount of gas, the new pressure will be double the old pressure. I say "in general" because this isn't exactly true, but it is close enough for the purposes of this teaser.

So my question is this: If you have a tire filled with the standard 32 psi and you double the amount of air molecules in the tire, what pressure will your tire gauge now read? Assume that the tire does not expand, and that the first sentence of this teaser is exactly true.

The answer is NOT 64 psi.

So my question is this: If you have a tire filled with the standard 32 psi and you double the amount of air molecules in the tire, what pressure will your tire gauge now read? Assume that the tire does not expand, and that the first sentence of this teaser is exactly true.

The answer is NOT 64 psi.

### Hint

Atmospheric pressure is about 15 psi. How does this affect the answer?### Answer

79 psi.Why? Because pressure gauges are set to read "0 psi" when the pressure being read is the same as atmospheric pressure. This is very convenient because you can easily tell from the gauge if the container is under pressure or vacuum. However, this also means that "0 psi" does not really mean that there is no pressure in the container - true zero psi occurs at full vacuum.

So to solve this problem, you have to recognize the fact that at 32 psi there are enough air molecules in the tire to increase the pressure from full vacuum (no molecules) to 32 psi. Since atmospheric pressure is about 15 psi, then the real pressure is 32 + 15 = 47 psi. Since this is the real pressure in the tire, you can now double it to get 94 psi. If the real pressure is 94 psi, the gauge will read 94 - 15 = 79 psi.

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## Comments

Excellent... except of course the tyre will probably burst and the gauge will then read 0 psi. Good one.

you didn't specify that this was taking place on earth. i thought it was in outer space.

Like said before i wouldn't sugguest a experiment. Good one.

Wow, I thought I had the right answer! Good teaser, I liked this one.

Could be much better

Ahh jesica doesn't know what she's talking about this was a great teasr and I got close to the answer I got 81.

Tangent: In outer space, would Jonnyonline's tire gauge work at all? Would a tire gauge's calibration be dependent on atmospheric pressure to push it in?

Almost every pressure gauge is dependent on the ambient pressure. The same pressure gauge that reads 32 psi on Earth would read 47 psi in space. You're absolutely right, Quax: on Earth there is 15 psi pushing into the gauge. When we say that something contains a pressure of 10 psi, what we REALLY mean is that it contains 10 psi more than the air around it.

wait given the tire stays the same volume wouldnt the gauge still read 32 in space cause it only measures the pressure inside the tire right...and the gauge is calibrated to subtract 15. The pressure inside the tire doesnt change if it's volume doesnt right?

You're right, worldnick, the tire pressure doesn't change if its volume doesn't. What's incorrect is your statement that the gauge is calibrated to subtract 15. It is NOT calibrated to subtract 15. It subtracts whatever the pressure outside the tire happens to be. On Earth, it happens to subtract 15 psi. In space, it subtracts 0 psi. 47-15=32 psi gauge reading on Earth, and 47-0=47 psi gauge reading in space.

I actually get 78.7 psi, when using 14.7 psi (the actual atmospheric pressure) instead of 15 psi. Great teaser - thanks!

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