Finding Pressure change as height changes with Pfinal given

• cnd4747
In summary, the question is asking if the pressure it would pop at is the difference between the internal and external pressures, which it is. The next question is how to treat the balloon, which is complicated and depends on the balloon. The final question is how to find the pressure difference, which is solved by using the P1V1=P2V2 equation and imagining a balloon with the minimum size to float.
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.

cnd4747 said:
My question is, is the pressure it would pop at the difference between the internal and external pressures?
In a word, yes.

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

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.

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.

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.

cnd4747 said:
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.

cnd4747 said:
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

cnd4747 said:
You are welcome

1. How does pressure change as height increases?

As height increases, the pressure decreases. This is because the weight of the atmosphere above decreases, causing a decrease in the number of air molecules and thus a decrease in pressure.

2. How can I calculate pressure change with a given final pressure?

To calculate pressure change with a given final pressure, you will need to know the initial pressure and the change in height. Using the equation P1/P2 = (h1/h2), where P1 is the initial pressure, P2 is the final pressure, h1 is the initial height, and h2 is the final height, you can solve for the pressure change.

3. What is the relationship between pressure and height?

The relationship between pressure and height is an inverse one. As height increases, pressure decreases and vice versa. This is due to the weight of the atmosphere above and the decrease in the number of air molecules at higher altitudes.

4. Can pressure change with height be measured in different units?

Yes, pressure change with height can be measured in different units such as Pascals, atmospheres, or millimeters of mercury. However, it is important to ensure that all units are consistent when using the equation to calculate pressure change.

5. How does temperature affect pressure change with height?

Temperature does not have a direct effect on pressure change with height. However, as temperature increases, the air molecules will have more energy and will be moving faster, leading to an increase in pressure. This can affect the pressure change calculation if the temperature is not constant throughout the height change.

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