A Valve is between two inequally inflated balloons. If we open the Valve, the air from the bigger balloon should go to the smaller one to make them equal, instead all the air goes in the bigger one.

Question

Please be gentle. I am not that smart.

In: 51

Answer 1

In a lot of systems the more you put in the harder it is to put the next little bit in. We might imagine filling a jar through a port at the bottom: the more water is in the jar the more pressure we have to overcome to keep putting water in.

In those sorts of systems if we set up this kind of problem we’d get the intuitive result. The fuller side is trying to push its contents out harder than the empty side, so material flows until the forces are equalized. This won’t necessarily happen when there’s an equal *volume*, but if they reach an equal *pressure* then everything will stabilize.

Balloons have a backwards relationship between pressure and volume, though. The hardest bit of air to get into a balloon is the first little bit that gets the rubber to stretch. From there it gets easier and easier to put more and more air in–up until right around the time it pops (balloons are grossly non-linear and really a pain to try to characterize mathematically).

So when you have less inflated balloon it’s trying harder to push its air out than a more inflated balloon is. Hook them together and the less inflated balloon will win the contest, pushing its air into the more inflated balloon.