Two identical balloons?

Question

where one is blown bigger are connected by the strow for pressure to equalize. Will the bigger balloon get bigger or smaller?
Please give the proof.

Answer 1

If r,a are the actual and initial (when it's empty) radius, then the potential energy of the balloon itself is:

E = (C/2)*(r-a)^2

for some constant C. A simple way to see this is to think of the balloon as a two dimensional network of springs (the potential energy of a spring is V = (k/2)(x-x0)^2) which linearly scale in size as the balloon does.

Treat the air as incompressible at least for a qualitative explanation (consider how difficult it is to blow air into a fixed container (such as a pop bottle) versus a balloon). In that case the guage or net pressure (difference from atmospheric pressure) just comes from the elastic force of the balloon. The relation between the volume of air inside and the radius is:

dV/dr = 4pi*r^2

So the relation between the energy and the volume of air inside it (which is the same as the pressure (dE = PdV):

P(r) = dE/dV = (C/4pi)(r-a)/r^2
= Constant * (1/r - a/r^2)

This function increases from 0 at r=a to a maximum at r=R=2a, and from there on decreases as the radius increases. The maximum may not occur exactly at 2a, but it probably increases up to some relatively small radius R and then decreases.

If two balloons are blown up to normal sizes (>R), air should flow from the smaller into the larger. In other words the small one gets even smaller until it goes below (the very small radius) R where the pressure begins to decrease with size.

Answer 2

Dr Greg couldn't have said it better.
Assuming the balloons were same elacticity, ect. Even if air was let out connecting them to the straw. They would equalize.
You could try this yourself, then at the end weigh each balloon, if the numbers are different, you have to think of what could have made them different.
-If you let out some air while tying.
-If you used string, were they identical types, lengths, ect?
-Is there a hole in one balloon?
And many other things.
But yes, they will equalize.

Answer 3

they will equalise.

the larger balloon is stretched more and so stores more elastic potential energy than the smaller balloon. this means that the larger balloon is pressing harder on its air (higher pressure).

when these 2 balloons are linked, equilibrium must be reached. some air will be forced from the larger to the smaller balloon until their volumes, hence their pressures become the same. this force is due to the pressure difference.

Answer 4

I could disagree with Daniel C. In equilibrium state the pressures in the balloons would be equivalent and which ability equivalent stretching of the two balloons. This in turn will cause them to of equivalent length and shape if of comparable constitutions.

Answer 5

It depends, Both balloons has a same Elasticity and size. the pressure become normal p1v1=p2v2

Answer 6

huh + what = ?