Finding Pressure change as height changes with Pfinal given

[cnd4747]

Hi, I am doing a project for school where I am calculating at what height a balloon would pop from pressure while rising.
At the point I am now, I have the initial pressure and the pressure it would pop at. I know work = pressure * change in volume, and that at some point I will need to use the barometric equation, but I do not know how to get there. I understand that as the balloon rises, the atmospheric pressure around it decreases while its internal pressure stays the same (or actually increases if its volume becomes smaller due to temperature change). My question is, is the pressure it would pop at the difference between the internal and external pressures?

The eventual goal of my problem is to find at what height the balloon would pop, given I know the pressure it would pop at.

Sorry if this is confusingly worded or poorly explained.

 

[Bystander]

My question is, is the pressure it would pop at the difference between the internal and external pressures?

In a word, yes.

 

[cnd4747]

I'm not sure I understand what you mean, Bystander. To be totally honest, I'm not extremely familiar with thermodynamics. I'm just not sure which equation to use? would I use (p1v1)/(p2v2) = (n1T1/n2T2)? The problem is that I'm not really sure where to start

 

[cnd4747]

I think what I'm going to do is this: the minimum amount for a balloon to float is density of air * volume - density of helium * volume - mass of balloon, and if that's <0 it will float. From there I'll find p1 at that volume and plug it into p1v1=p2v2 to get an idea of the volume at the point it would blow up. But I'm still not sure how to finish.

Also, what is the name of the law I am using with the mass and density of helium? I can't remember what it is called.

 

[Cutter Ketch]

P1V1=P2V2 is only true at constant temperature. If you would like to include temperature change with altitude as it sounds like you do, then you should use the ideal gas law.

The next question is how to treat the balloon. Suppose the balloon will stretch to a given volume with very little effort. Then the pressure inside the balloon equals the pressure outside. You easily work out the volume and the balloon will rupture when it exceeds a limiting volume.

Now suppose the balloon won't expand at all. Except for the temperature change the pressure inside stays constant and the balloon ruptures when the pressure difference exceeds some limiting value.

The problem is that a real balloon is somewhere in between these two. Some are closer to one case or the other. To do this properly you would need to know the extra pressure as a function of volume imparted by the elasticity of the balloon. However in many cases you may be able to approximate one or other extreme. For a regular latex balloon I'd use the former. When you are blowing up a balloon after the initial difficulty it doesn't require much more force as the balloon gets bigger. So say the pressure inside is the same as outside and determine the volume.

 

[cnd4747]

Thank you Cutter. So if it's dependent on volume then do I even need the pressure it blows up at then? Even though it's less likely, I think I'll base it off pressure since that's what I've been basing it on anyways. How do I solve for pressure difference in the sense you are talking about? Or since I'm using standard little balloons would the difference be big enough that I should use volume change and just ignore the pressure?

Sorry for all the questions but I'm just pretty confused.

 

[cnd4747]

Or could I do (P1V1)/T1 = (P2V2)/T2. I have both the final pressure and the final radius, from which I could get the final volume, and then solve for T2?

What I think I'm going to do is imagine I have a balloon with the minimum size to float and then put it in the equation up there solving for T2. But then my problem is that I still don't know at what point the balloon will pop, just the temperature. And I haven't really been able to find a formula relating altitude and temperature.

 

[Cutter Ketch]

Thank you Cutter. So if it's dependent on volume then do I even need the pressure it blows up at then? Even though it's less likely, I think I'll base it off pressure since that's what I've been basing it on anyways. How do I solve for pressure difference in the sense you are talking about? Or since I'm using standard little balloons would the difference be big enough that I should use volume change and just ignore the pressure?

Sorry for all the questions but I'm just pretty confused.

I see, you want a way to say at what pressure difference or what volume increase a balloon will pop. That is a property of the strength of the material, and there won't be a simple equation for it. I'm not going to start you down that road. You can just claim that you know the value or at least that it is knowable, or if this is more experimental you can go get a bunch of balloons ad overfill them to see where they pop.

Regarding whether you fail due to pressure difference or exceeding the maximum volume, you have to decide whether your balloon is stretchy or not. If it is stretchy then the internal volume will grow to keep the inside pressure about equal to the outside pressure and it will fail when that is too big. If it isn't stretchy the volume and pressure will stay the same as they were on the ground. The balloon will rise until the pressure difference ruptured it.

 

[cnd4747]

I have the stress and strain of the material, along with Young's Modulus and Poisson's ratio. Can I find it based on that?

Overfilling them was actually part of my experiment, that's how I found the rupture radius and volume, young's modulus, etc.

 

[Cutter Ketch]

Or could I do (P1V1)/T1 = (P2V2)/T2. I have both the final pressure and the final radius, from which I could get the final volume, and then solve for T2?

What I think I'm going to do is imagine I have a balloon with the minimum size to float and then put it in the equation up there solving for T2. But then my problem is that I still don't know at what point the balloon will pop, just the temperature. And I haven't really been able to find a formula relating altitude and temperature.

T vs altitude (typical) is known or can be looked up. P vs altitude (typical) is known or can be looked up or determined with your barometric equation. What you are solving for is V2, and I believe you said you do know at what V the balloon will pop.

 

[cnd4747]

Thanks for all your help!

 

[Cutter Ketch]

Thanks for all your help!

You are welcome