Help with this statement?

[m25]

"As balloon rises to a high altitude, the atmospheric pressure decreases while the internal pressure of the balloon stays constant, creating a larger and larger DIFFERENCE in pressure across the balloon's membrane. This increases the volume of balloon until it can no longer expand and finally pops."

So conceptually, I understand the reason balloon expands is because the pressure pushing on the balloon's membrane from the inside(internal pressure) is greater than the pressure pushing the balloon from the outside(atmospheric pressure). But is it possible to prove this by using some kind of formula, such as PV=nRT? Or am I understanding it wrong?

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[Cawolf]

Well we know from the ideal gas law that P1V1 = P2V2.

As the balloon rises to a lower pressure part of the atmosphere, the volume will increase to keep PV constant - assuming it rises slow enough to be isothermal (which it likely will, or we assume it does). The volume will increase until the elastic stress placed on the balloon causes the material to fracture.

This is occurring because the pressure in balloon causes the balloon to expand until the pressure matches the atmospheric pressure. It will expand until the pressure of the gas inside the balloon is at equilibrium with the outside pressure due to the elastic nature of the balloon.

 

[m25]

Well we know from the ideal gas law that P1V1 = P2V2.

As the balloon rises to a lower pressure part of the atmosphere, the volume will increase to keep PV constant - assuming it rises slow enough to be isothermal (which it likely will, or we assume it does). The volume will increase until the elastic stress placed on the balloon causes the material to fracture.

This is occurring because the pressure in balloon causes the balloon to expand until the pressure matches the atmospheric pressure. It will expand until the pressure of the gas inside the balloon is at equilibrium with the outside pressure due to the elastic nature of the balloon.

What you are saying makes sense conceptually but I am still confused about the equation.
So what do P1, V1, P2, and V2 stand for in this case?

 

[Cawolf]

The pressure and volume in the balloon at the ground (1) and just before it explodes (2). If you prefer to integrate it then it is the constant, slow, reversible change in volume as the balloon ascends due to decreased external pressure.

It really is a conceptual issue. Gas has no set volume unless confined by a container, and a balloon offers no barrier to expansion other than the pressure exerted on the balloon by the atmosphere. When the external pressure decreases, the pressure in the balloon "matches" it (because pressure is not constant here). The decreased pressure in the system (balloon) can be approximated by the ideal gas law to show that a proportional increase in volume will occur.

 

[m25]

The pressure and volume in the balloon at the ground (1) and just before it explodes (2). If you prefer to integrate it then it is the constant, slow, reversible change in volume as the balloon ascends due to decreased external pressure.

It really is a conceptual issue. Gas has no set volume unless confined by a container, and a balloon offers no barrier to expansion other than the pressure exerted on the balloon by the atmosphere. When the external pressure decreases, the pressure in the balloon "matches" it (because pressure is not constant here). The decreased pressure in the system (balloon) can be approximated by the ideal gas law to show that a proportional increase in volume will occur.

So you are saying that internal pressure of balloon is not constant throughout, that it tries to match with outside pressure by increasing volume(which decreases internal volume)?
So basically, as balloon ascends, the internal pressure of balloon decreases at the same rate as the atmospheric pressure(by expanding it's volume until it can no longer expand and pop)?

But why does balloon even try to match outside pressure?

 

[Cawolf]

The inside pressure is the equal to the outside pressure.

It's just how it is with a flexible container.

 

[Cawolf]

Maybe it would be more intuitive if you tried to think of why they would not be equal? What stops something normally from being the same pressure as it's environment? A container that is rigid and does not "transmit" the pressure from outside to inside. A balloon is just a segregation of some gas molecules that is the same pressure as it's environment.

Or think of the converse, blowing a balloon up. It starts with almost no volume so that it's pressure is atmospheric. As you add gas moles into it, it expands so that the pressure remains constant.

 

[m25]

The inside pressure is the equal to the outside pressure.

It's just how it is with a flexible container.

Oh okay. So something like car tires (which I assume is not as flexible) will maintain the pressure difference between inside and outside, but balloons don't?

 

[Cawolf]

Right, a tire has some structural stability. They don't become flat when deflated.

This is of course an ideal approximation of a balloon. For the purposes of quantitative gas chemistry it is a good model though.