[Physics] Why are volume and pressure inversely proportional to each other

ideal-gaspressurethermodynamicsvolume

It makes sense, that if you have a balloon and press it down with your hands, the volume will decrease and the pressure will increase. This confirms Boyle's Law, $ pV=k=nRT $.

But what if the pressure in the balloon increases? Doesn't it make sense that the balloon would want to expand? That is, that as pressure increases, volume increases. This seems to contradict Boyle's Law.

Could you explain what I'm doing wrong in the second scenario?

Could you give an example that does confirm Boyle's law?

Best Answer

Pressure and volume have an inverse relationship when $n$ and $T$ are constant. How do you imagine the pressure in the balloon is increased? Either $n$ or $T$ must increase, or $V$ must decrease.

Additionally, balloons are roughly constant-pressure systems. The rubber membrane is a very weak elastic, so the internal pressure of the balloon is at almost constant pressure, just above atmospheric. When you squeeze a balloon, you usually don't change the pressure or volume much, because the rubber just expand in an area where you aren't pressing.

Since you edited your question to ask for an example of Boyle's Law: Consider a piston in a cylinder. As the piston is pushed in, the gas in the cylinder is forced in to a smaller volume, and its pressure increases. If this is done slowly enough that no significant heating of the gas occurs, the relationship of pressure and volume will follow Boyle's Law.