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# Volume Of a Sphere, vs Pressure

04/12/2022 9:20 AM

OK say you have a sphere with a volume of 14 cubic meters.

How much volume do you need to add to this sphere so the pressure differential inside vs outside of the sphere has 0.4 PSI now?

Thanks!

Joe

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#1

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 9:24 AM

If the wall is a liquid, it depends upon the surface tension.

If the wall is a solid, it depends on its modulus of elasticity and its thickness; if it is made of thin rubber, then rather more volume will be needed than if it is made of thick steel.

It also depends upon temperature. Adding volume to increase the pressure will also increase the temperature.

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#2

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 9:46 AM

Morning PW,

HI!

Yeah Mr. Balloon here. think a non stretching sphere. Yeah I know the temp will rise some, but at that pressure difference I don't think it would be much.

Joe

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#3

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 9:58 AM

Probably don't need to add any at all, just raise the temperature a bit..

https://opentextbc.ca/chemistry/chapter/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law/

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#4

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 10:22 AM

<....non stretching sphere...>

This universe doesn't work that way.

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#5

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 10:23 AM

It also depends on the nature of the stuff that is being added to the <...sphere...> to create the pressure difference.

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#6

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 10:24 AM

Exactly. Zero needs to be added if the temperature change is adequate. GA

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#7

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 10:38 AM

Assume the sphere initially has 14.7 psi.

Assume the temperature remains the same.

P1V1/T1 = P2V2/T2 or P1V1 = P2V2 : V2=V1*P1/P2

V1=14, P1=14.7, P2=14.7-0.4=14.3

V2=14 * 14.7 / 14.3 = 14.39 cu meters

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#8

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 10:44 AM

Ok it Looks like I need to give more details.

The sphere is at 60K feet ambient air pressure is 1.040159 Psi

temp is, -56 C

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#9

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 11:50 AM

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#10

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 11:51 AM

...and what gas is inside the balloon?

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#11

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 11:57 AM

oops ambient "AIR" whatever The surrounding air around the sphere is made of.

Joe

And Thanks everyone!

Joe

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#12

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 1:23 PM

If temp is constant, pressure is inversely proportional to volume. Boyle's law works at any altitude.

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#13

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 7:30 PM

~0.33 psi is the atmospheric pressure at that altitude and temperature...

https://www.mide.com/air-pressure-at-altitude-calculator

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#14

### Re: Volume Of a Sphere, vs Pressure

04/12/2022 11:23 PM

Why not use simplifying assumptions. Sorta like the frictionless pulleys in physics class. Therefore, a non-stretching steel sphere with no temperature rise. Then refine if you want.

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#15

### Re: Volume Of a Sphere, vs Pressure

04/13/2022 8:16 AM

=72 millibar...

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#16

### Re: Volume Of a Sphere, vs Pressure

04/13/2022 8:17 AM

=23 millibar...

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#17

### Re: Volume Of a Sphere, vs Pressure

04/13/2022 8:18 AM

=28 millibar...

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#18

### Re: Volume Of a Sphere, vs Pressure

04/13/2022 8:27 AM

It looks like at this juncture, the forum cannot agree on the ambient air pressure.

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#19

### Re: Volume Of a Sphere, vs Pressure

04/13/2022 8:29 AM

<...assumptions...want...>

A better definition of the problem would avoid the need to guess these things.

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#20

### Re: Volume Of a Sphere, vs Pressure

04/13/2022 9:17 AM

My Calculator at 60K feet says 71.71641 millibar

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#21

### Re: Volume Of a Sphere, vs Pressure

04/13/2022 10:11 AM

OK. So assuming the <...sphere...> doesn't change shape and the compression is isothermal, the <...volume...> needed at 72 millibar to raise the pressure to 100 millibar is 28/72x14m3.

However, it would take a substantial support structure at that altitude to support a <...sphere...> that doesn't change shape measurably as the internal pressure is raised by 100/78=28%, and the forum has no information about this.

Assuming it is a rather more flexible material <...Balloon...> and can change shape, the strength and the buoyancy of the material forming the <...sphere...> is also a factor for, as the pressure inside it increases and its volume increases, its weight does as well, therefore it becomes less buoyant and it is therefore likely to assume a lower altitude, thereby changing the volume and the pressure inside it during the descent.

Given the lack of clear starting conditions it is now easier to see how intractable this problem actually is.

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#22

### Re: Volume Of a Sphere, vs Pressure

04/14/2022 4:17 AM

Oh, and because it drops to a lower altitude, the ambient temperature goes up, which makes it expand as it does so.

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#23

### Re: Volume Of a Sphere, vs Pressure

04/15/2022 1:55 AM

So, much like filling a tire. Don’t think the shape, I.e. sphere matters?

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#24

### Re: Volume Of a Sphere, vs Pressure

04/15/2022 12:35 PM

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