If Pressure is inversely proportional to volume, theoretically, how does a tire burst if you pump too much air in it? If the volume inside the tire is increasing shouldn’t the pressure decrease?
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I’m not sure I understand your question.
The volume inside the tire *doesn’t* increase until it bursts. The pressure just goes up and up and up until it’s too much for the tire to contain, then it bursts. It’s only after it bursts that the pressure can go down.
You’re forgetting an important part of that. In a closed system like a tire, volume can’t increase. So as pressure increases, volume remains the same (ok, slightly increases, but not enough to relieve the overpressure)
The pressure does decrease when the volume in the tire increases.
However, the volume in the tire does not increase when you pump air into it – that would require the tire to physically get bigger which only really happens as it bursts.
The equation for an ideal gas is:
𝑃𝑉=𝑛𝑅𝑇
P = pressure.
V = volume.
*n* = amount of substance.
R = ideal gas constant.
T = temperature.
Rearranging this gives:
𝑃=𝑛𝑅𝑇(1/𝑉)
So 𝑃 is only inversely proportional to 𝑉 if the constant of proportionality, 𝑛𝑅𝑇, is a constant. And that is a constant only if n (the amount of stuff) is constant. If the amount of stuff changes (ie. you’re pumping it with air) then pressure is not inversely proportional to volume.
Pressure is inversely proportional to volume if the amount of gas (and the temperature) remains constant. Imagine a balloon with a set amount of air inside it: if you squish the balloon, the volume of the balloon decreases, but the pressure increases (it becomes harder to keep squishing, disregarding the fact it kind of stretches out to the sides in an attempt to increase volume).
With a tyre, any air you put into the tyre is going to increase the pressure in the tire. That pressure is going to push on the tyre walls and increase the volume, thus decreasing the pressure in step. But you’re still adding more air in, and the tyre can’t get infinitely large, so eventually the volume stops growing and the pressure starts building. If the pressure gets to large that it overcomes the strength of the tyre, then you get an explosion.
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