### 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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