Boyle's Law: Air Volume Question

[Eastwest]

There is a question still willing to debate that volume and pressure is 100% absolute . A tank with exactly 3000 psi of air pressure will have absolute 50% volume at 1500 psi . It seems to be missing density with this equation ?

 

[inquis]

There is a question still willing to debate that volume and pressure is 100% absolute . A tank with exactly 3000 psi of air pressure will have absolute 50% volume at 1500 psi . It seems to be missing density with this equation ?

What you have called volume is more correctly termed the number of molecules. Alternatively, you can call it "surface volume", as it's that's the volume the contents would occupy at sea level (1 atm). Yes, the density is lower at 1500 psi, because there are fewer molecules but the tank volume is effectively unchanged.

Even with that correction, the answer is no, you will have more than half the molecules at half the tank pressure due to non-ideal gas behavior. Air has about 97% the ideal quantity at 3000 psi. That shortage depends on the type of gas. Check out "Z factors".

 

[BRT]

There is a question still willing to debate that volume and pressure is 100% absolute . A tank with exactly 3000 psi of air pressure will have absolute 50% volume at 1500 psi . It seems to be missing density with this equation ?

Forgetting "Z" factors which are fairly small at 3000# the 1500# tank will have half the gas density and half the air molecules as the 3000# tank. A 15 liter tank with the valve off has 15 liters of air at ambient pressure. Assuming ambient is sea level, pumping in enough air to raise the pressure 1 bar (1 atmosphere) will double the air molecules in the tank.

 

[admikar]

I'm more interested in why we have resurected 13 years old thread?

 

[lowwall]

I'm more interested in why we have resurected 13 years old thread?

It's only 4.33 years at 20m.

 

[marcus213]

Thank you, thank you, thank you! To all. OMG, i've beat my head against the wall about this issue with other divers for years! There's no WAY that a Alum/Steel scuba tank filled with comp air that's about to POP, is going to compress down at a divers depth. Yes i agree TEMP could change tank press. IF so, your tank would be crushed like the little plastic soda bottle or the beach ball!!! It occurs somewhere in the reg or breath, when the air really sees, hey i'm under Atmos/Bars of pressure. Now with your soft body tissue/lungs crushed down like the BEACH BALL going down to depth, the lungs need more air to fill up to GODS spec,s for giving proper air volume to support human body with Oxygen supply, like at the surface. Which means you suck more GAS to fill those squeezed lungs, to fill em up full!! Finally common sense & Phys prevails!!

 

[boulderjohn]

This can confuse even some very experienced divers.

Not too long ago, a cave diver died when he ran out of air not too far from the exit of the cave. This cave has a very steep section right at the entrance, so if he had gotten just a little farther, he would have reached that steep ascent to the entrance. A very well known diver commented on that, saying that if he would have gotten only a little farther and started the ascent, he would have benefitted from expansion of the air left in his tank and possibly made it the rest of the way out.

Well, he might very well have made it the rest of the way out because of the ascent, but not because the air in the tank (or the hoses) was expanding. The gas in a rigid container like a scuba tank is not affected by pressure changes. What is affected, however, is the regulator. A regulator is designed to deliver its air at a pressure slightly higher than the water pressure. As it gets near empty, it does not have enough pressure to deliver air at the pressure the diver is under at depth. When the diver ascends, there will now be enough pressure in the tank to deliver air at the decreased pressure of the ascent.

 

[Caversluis]

There is a question still willing to debate that volume and pressure is 100% absolute . A tank with exactly 3000 psi of air pressure will have absolute 50% volume at 1500 psi . It seems to be missing density with this equation ?

Actually, it is not 100% absolute. Most of the time we calculate as if the gas behaves like an ideal gas, because it is easier to calculate (it is linear). But real gasses behave differently.

You can read a lot more about it in this Wikipedia article.

At pressure higher than 200 bar, the difference can be significant. When using 300 bar cylinder, you will only gain the equivalent of 70 bar for the last 100 bar.

This effect is much more significant than the density impact.

 

[John C. Ratliff]

The amount of gas in the cylinder will not change because of depth. What changes is the density of the air that is breathed. At 33 feet, or 10 meters, the air density coming out of the regulator is twice that at the surface. At 99 feet, or 30 meters, the pressure is 4 times that of the surface, so when you breath the regulator provides air that is 4 times as dense as at the surface.

So if your air consumption is, say, 2 cubic feet per minute at the surface, you will consume out of that cylinder 4 cubic feet per minute at 33 feet, or 10 meters. At 99 feet, or 30 meters, your air consumption will be four times your consumption rate on the surface. So at 99 feet, or 30 meters, your air consumption at 4x the surface will be 2 cfm x 4, or 8 cubic feet per minute.

Now, if you have an 80 cubic foot cylinder, on the surface at 2 cubic feet per minute, you can breathe from it for:

80 ft3 / 2 ft3/min = 40 minutes

If you use that same 80 cubic foot cylinder at 99 feet, or 10 meters, your will consume air at 2 cubic feet per minute times 4, or 8 cubic feet per minute. This is because the air delivered by your regulator is 4 times as dense as on the surface. So:

80 ft3 / 8 ft3/min = 10 minutes of air

it has nothing to do with the air inside the tank being "compressed," but rather with air being delivered at different densities so as to me at equal pressure to the water at that particular depth.

Now, concerning the diver who ran out of air at almost the entrance to a cave, and saying that the diver would have made it to the surface if he/she had been able to ascend, that is not entirely true. As boulderjohn stated above, there is lessening pressure, but that lessening pressure would only be enough to allow a few breaths. Let's again say that this diver was at 99 feet near the entrance of the cave, and started ascending with an empty tank. An 80 cubic foot tank has a volume of 0.4 cubic feet. The Chairman did this calculation, as follows:

an AL80 tank holds 80 cf at 3000 psi (3014.7 psia)

80 cf/3014.7psi = 0.0265 cf/psi

0.0265 cf/psi x 14.7 psi/ata = 0.390 cf/ata

So your al80 tank has almost 4 tenths of a cubic foot as it's internal volume. You can do the math for your lp tank in precisely the same way.

Internal Volume

In an earlier thread, FredT stated: "The amount of air a tank holds is related to it's INTERNAL volume, not the external size of the tank." :confused: So, when we talk about an AL80 tank, are we talking about the internal volume or the external displacement? Next step, how do I compare the...

scubaboard.com

If a diver is out-of-air at 99 feet, and there is an expansion of 4x on the way to the surface, he/she will gain about 4 x 0.4 cubic feet = 1.6 cubic feet of air to be breathed. But this would only be available at the surface. The air could be sipped as the diver ascends, but there would not be enough to do any decompression, or even a safety stop.

SeaRat