# The Naked Scientists Forum

### Author Topic: What volume of air is stored at different pressures?  (Read 5218 times)

#### Ethos_

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##### What volume of air is stored at different pressures?
« on: 26/07/2014 21:10:10 »
I have a question about the volume of air that can be contained at various pressures.

Assuming we have a cylinder of 10 gal. capacity and we pressurize it to 120 psi with air, how many cu/ft of air will it contain at that pressure?
Secondly, using the same 10 gal. cylinder, we now pressurize it to 7000 psi. How many cu/ft of air will the cylinder now contain pressurized to 7000 psi?

These tests are of course both done at the same 72 degrees F. temp.

I need some help from a Mechanical Engineer on this question.

Thanks...............................Ethos
« Last Edit: 29/07/2014 08:04:10 by chris »

#### CliffordK

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##### Re: How many cu/ft........
« Reply #1 on: 27/07/2014 07:12:09 »
The first step I would do is to convert gallons into cubic feet.

So, 1 gallon = 0.133681 cubic feet.  10 gallons = 1.33681 cubic feet.

Now, there would be a few ways to solve your problem.  Remember for an ideal gas, PV=nRT.  Assuming you keep Temperature constant.  So, pressure and volume are related linearly.  Increase the pressure by 10x in a fixed container, and the volume of gas held by that container increases by 10x.

So, I would convert PSI to ATM (or BAR).

1 ATM =  14.69595 PSI.

So, 120 PSI = 8.17 ATM.  Now, typically PSI does not include the static atmospheric pressure, so to make the calculations easier, add 1 more ATM, so one gets 1 ATM == 9.17 ATM.

Multiply that times your volume above,  1.33681 Cubic Feet, and you get:
9.17 ATM x  1.33681 CF in container = 12.3 Cubic Feet of air contained in the 10 gallon container at 120 PSI.

I'll leave the calculations at 7000 PSI to you.

#### Ethos_

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##### Re: How many cu/ft........
« Reply #2 on: 27/07/2014 13:23:07 »

Assuming you keep Temperature constant.  So, pressure and volume are related linearly.

I'll leave the calculations at 7000 PSI to you.
Thanks CliffordK, I wasn't sure whether the math was linear or not.

#### chiralSPO

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##### Re: How many cu/ft........
« Reply #3 on: 27/07/2014 14:04:30 »
Time for some pedantry...

Well, a linear relationship is only a first order approximation. With air at those pressures, it is perfectly fine to make this assumption for most applications (it depends how much precision is required). Remember that PV=nRT only applies to ideal gases. If one takes into account the volume of the molecules and their interactions, actual measurements can diverge quite significantly from a linear relationship, especially at high pressures and/or low temperatures.