how much air in the tank?

[Crush]

Have you ever wondered how much air is REALLY in your tank? If so, don't trust your pressure gauge - it is misleading you.

In basic scuba we learn ideal gas laws: PV=nRT and variants thereof. While the mixes that we breathe behave largely as ideal gasses, there are in fact deviations from ideal gas behaviour. These deviations can be formulated in many different ways. One way is the van der Waals gas equation: (P + n^2 a/V^2) (V - n b) = n R T where a and b are respectively the coefficients which account for the attraction between gas particles (atoms or molecules) of the same type and the volume of the gas particles (atoms or molecules). Using the gas constants:
a[N2] = 1.370;
b[N2] = 0.0387;
a[O2] = 1.382;
b[O2] = 0.0319;
a[Ar] = 1.355;
b[Ar] = 0.0320;
and an atmosphere composed of 78.09% nitrogen, 20.95% oxygen, and 0.93% argon (other gases were omitted) and assuming no interactions between molecules/atoms of different types I crunched the numbers to see how far-off the ideal gas law was from what I might be sipping out of a tank. I also ran the numbers for EAN 36.

The amount of gas in your tank if the gas behaves as an ideal gas, your tank volume is 100 L, and your tank pressure is 206.842 bar (3000 psi) at 298 Kelvin (25 C) is 834.82 moles of gas. Fixing the number of moles (or molecules) of gas at 834.82 moles and varying the tank volumes (in litres), I observed the pressure fluctuations for both an ideal gas (Pideal) and a van der Waals approximation (PvdW), both in units of psi. The values are shown below, as well as a percent error.

Summary: real gases are less compressible than are ideal gases at high pressures. For air at pressures above 3000 psi there are in fact fewer molecules of mix than your pressure gauge would lead you to believe if you think PV=nRT. EAN 36 seems to compress better - its pressure has to be above 3333 psi for you to have fact fewer molecules of mix than your pressure gauge/PV=nRT would imply. Also, real gases attract one another more than do ideal gases (which don't interact), making the gas more "compact" at lower pressures. At pressures below 3000 psi for air (or 3333 psi for EAN 36) there is more air in your tank than you would lead to believe based upon PV=nRT and your pressure gauge.

Do you care if you are not a geek? Probably not. That is why I care.

Air:
V Pideal PvdW %error
70 4286 4874 -12.1
80 3750 3963 -5.38
90 3333 3378 -1.32
100 3000 2965 1.19
110 2727 2654 2.75
120 2500 2410 3.74
130 2308 2211 4.35
140 2143 2046 4.72
150 2000 1906 4.94
160 1875 1785 5.05
170 1765 1679 5.09
180 1667 1586 5.07
190 1579 1503 5.03
200 1500 1429 4.97
210 1429 1362 4.88
220 1364 1301 4.79
230 1304 1246 4.70
240 1250. 1195 4.60
250 1200 1148 4.50



EAN36:
V Pideal PvdW %error
70 4286 4707 -8.95
80 3750 3856 -2.76
90 3333 3304 0.90
100 3000 2910 3.08
110 2727 2612 4.40
120 2500 2377 5.18
130 2308 2185 5.63
140 2143 2024 5.87
150 2000 1887 5.97
160 1875 1769 5.99
170 1765 1666 5.95
180 1667 1574 5.87
190 1579 1493 5.77
200 1500 1420 5.65
210 1429 1354 5.53
220 1364 1294 5.40
230 1304 1239 5.27
240 1250 1189 5.14
250 1200 1143 5.01

 

[Randy43068]

Yes
.
.
.

 

[tomboyy]

Now thats my idea of a basic scuba discussion

 

[DevonDiver]

I have literally no idea what you are saying.... but good work nonetheless

 

[Crush]

I have literally no idea what you are saying.... but good work nonetheless

Neither do I.

I was just curious to see what the answer was. The fact that the deviations from ideal behaviour are in many cases smaller than the uncertainty in my SPG has not escaped me...

 

[DevonDiver]

There was an answer? I couldn't even work out what the question was

 

[TSandM]

Interesting, and thanks for doing the math! I'd always read that, at our working tank pressures, the deviations from ideal were small, but they're actually larger than I thought. Not enough to change anything about how I do my dives, though; if I were ever to plan a dive where I carried no more than 5% more gas than I calculated I'd need, my buddy should take me straightaway out of the water!

 

[LoonDiver]

Ummm...so in English, this means there is more air in our tank than we think based on the SPG, or is it the other way around? I'm with DevonDiver, I had a hard time even understanding the question. I guess that means I'm not a geek??!!

 

[Steve50]

be careful you don't suck all the fun out of diving

 

[Crush]

I guess that means I'm not a geek??!!

Consider yourself blessed.

1. The pressure gauge is right. The assumption that the pressure is directly proportional to the amount of gas is incorrect, but that error is, in fact, small.

2. At low pressures real gasses are more "compact" than ideal gasses. This means that, at pressures below say 3000 psi, there are more gas particles in your tank than is predicted by the ideal gas law.

3. At high pressures real gasses are less "compact" than ideal gasses. This means that, at pressures above say 3000 psi, there are fewer gas particles in your tank than is predicted by the ideal gas law.

A practical example: which contains more gas mix - one "80L tank" charged to 2000 psi or one "40L tank," charged to 4000 psi? Answer: one "80L tank" charged to 2000 psi since at pressures above 3000 psi the gas gets less compressible. It took fewer gas particles to raise the pressure from 2000 psi to 4000 psi than it took to raise it from 0 to 2000 psi. The pressure went up to 4000 psi, it is just that it took fewer gas particles to achieve that than you would have thought. Putting less gas in to raise the pressure from 2000 to 4000 psi means you get less gas out as you reduce the pressure (by breathing) from 4000 psi to 2000 psi.