# Volume and Pressure

MastaFace
Hi people. I need some assistance for a problem that is beyond me. If I have a container that measures one cubic foot, and I fill it to 100 PSI, how many cubic feet of air is it holding? I'm not a student and you're not doing my homework for me, this is for an air tank I am building and I don't know the math. Thanks in advance for any assistance you can offer. If this is the wrong place to ask this question, please accept my apologies.

Dave

## Answers and Replies

Staff Emeritus
Science Advisor
Gold Member
Moving to general physics...

Science Advisor
You need to specify something extra for the question to make sense. A one cubic foot container contains one cubic foot of air, by definition. Are you asking how what volume of air at a certain temperature and pressure would you need to bring the pressure in the one cubic foot container to 100 PSI? Or conversely are you asking what volume one cubic foot of air at 100 PSI would fill at room temperature and pressure? Are you always talking about room temperature and pressure or some other temperature and pressure?

Staff Emeritus
Science Advisor
Gold Member
I suspect the OP wants to know the volume of air it takes at STP. This volume would be roughly 100/14.7 (about 6.8) cu. ft. It follows from Boyle's Law PV = constant.

MastaFace
OK. Temperature is constant, room temp. The container hods one cubic foot at room temp, sea level air pressure. If I pumped air into it at room temperature, sea level, how much air would I be adding to make the gauge read 100 PSI?

Science Advisor
Like Gokul already mentioned, it's solved using Boyle's law:

$$P_1 V_1 = P_2 V_2$$

$$(14.7 \frac{Lb_f}{in^2}) V_1 = (100 \frac{Lb_f}{in^2})(1 ft^3)$$

$$V_2 = 6.80 ft^3$$

Since you are using it as a tank, that may or may not be a useable amount depending on what you are doing with the tank. Just thought I'd mention that. Good luck.

Science Advisor
Gokul answered your question in anticipation. Boyle's Law says PV=const. so the volumes will be in the same ratio as the pressures. As 1 atmosphere pressure is 14.7 PSI, you require 100/14.7 * 1 cubic foot = 6.8 cu. feet of standard pressure air (assuming you want to keep everything at the same temperature, of course.)

MastaFace
Thanks all. That answers my question.

quark
Note that the pressure terms are absolute. If 100PSI is gauge reading then volume the container holds is 114.7/14.7 = 7.8cu.ft

Gold Member
I hope MastaFace doesn't blow him/herself up. Fiddling with tanks and pressures can be dangerous and requires due attention to safety precautions, and he/she doesn't seem to know a lot about it...

Science Advisor
Gack. Good catch on the mistake Quark. I wish I could edit my original post.

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