how much air in the tank?

[Crush]

I'll bet that when the SPG hits 0, you will straight away be looking for another tank to breathe from.

Bob
----------------------------------
I may be old but I’m not dead yet.

I stand corrected - when the SPG hits zero, then I know exactly how much usable air I have! Good point, Bob.

 

[Bob DBF]

I did actually appreciate the the thought and the work you put into posts, but I am after all a smartass.

Bob

 

[h90]

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.

I have a other example:
You have a 10 liter tank (for easier calculation) at 200 bar: so you think you have 2000 barl (or cpm) air.
As it is never enough and you don't like a big tank you buy a 300 bar tank and calculate 300x10=3000 barl.
So you are happy that you have 50 % more air.

But it is wrong
200 bar: 10x200/1.03=1941
300 bar: 10x300/1.11=2702
(correction factor for 25 degree Celcius taken from the book "Tauch-Theorie" from Thilo Kuenneth)
In fact you have only 40 % more air

If we dive in 50 years with a 450 bar system it is even worse
450 bar: 10x450=4500 expected but real just 3540
So if you use your SPG to know the amount of air by measuring the pressure you are 100 bar wrong. And it get worse as higher the pressure is.

 

[watboy]

I think that is not how to calculate standard error as that arises from sampling.

Also, the major issue is that you have assumed that VDW is correct, that the Ideal Gas law is incorrect and that the difference between the two amounts to a breakdown of the ideal gas law. I contend that at the pressures and temperatures involved, the ideal gas law is the more accurate model of the two. Your analysis has merely shown the difference between two models, and not the break down of either.

1. My a and b parameters were parametrized within the pressure range that I was calculating. There was no extrapolation. Since standard errors were not given, I assumed the last digit to be +/- 1.

2. I did a propagation of errors analysis (Taylor series expansion). All the usual caveats apply: no cross-correlations, no higher order terms, etc..

3. Critics have thus far failed to seize upon a major issue - there are not attractive "a" terms in the vdW system for hetero-molecular attraction. I state this for the second time and offer my numbers as the best-possible right now. They are an approximation, but they are better than the ideal gas approximation.

4. The take-home message is that, even if my numbers have infinite accuracy, they indicate that the break-down in ideal-gas behaviour is commensurate with SPG accuracy.

 

[Crush]

I think that is not how to calculate standard error as that arises from sampling.

If the a and b parameters were obtained in the pressure and temperature range of interest, and if the values were reported to the correct number of significant figures, the error expansion should work.

Also, the major issue is that you have assumed that VDW is correct, that the Ideal Gas law is incorrect and that the difference between the two amounts to a breakdown of the ideal gas law.

I am assuming that both are incorrect. However, I feel that the former is less incorrect than the latter. If their respective errors correlate, I have underestimated the difference between real and ideal. If their respective errors anti-correlate, I have overestimated the difference between real and ideal.

I contend that at the pressures and temperatures involved, the ideal gas law is the more accurate model of the two. Your analysis has merely shown the difference between two models, and not the break down of either.

Your trust in PV=nRT is admirable. I might even share it...

That the ideal gas law breaks down at high temperatures and pressures is known. The question is, how much? My analysis has shown a difference between two models. My assumption is that one model reflects reality better than the other. As stated earlier, the actual experiment is more difficult to carry out. Perhaps we should defer to NOAA...

 

[watboy]

Perhaps this is just an issue of symantics. But standard error is a statistical measure measuring the variance in the data from repeated sampling or measurement. That you did a calculation, means there is only one data point. If you had done simulations or experimentations and had multiple data points, then you could provide standard error. With your method, I think your best bet is just to stick to significant figures.

We are not at the high temperatures where the breakdown of the ideal gas law is sufficient to warrant a new model. Its been over a decade, but if memory serves, for the pressures and temperatures involved, ideal gas law is quite accurate and the model engineers use.

If the a and b parameters were obtained in the pressure and temperature range of interest, and if the values were reported to the correct number of significant figures, the error expansion should work.



I am assuming that both are incorrect. However, I feel that the former is less incorrect than the latter. If their respective errors correlate, I have underestimated the difference between real and ideal. If their respective errors anti-correlate, I have overestimated the difference between real and ideal.



Your trust in PV=nRT is admirable. I might even share it...

That the ideal gas law breaks down at high temperatures and pressures is known. The question is, how much? My analysis has shown a difference between two models. My assumption is that one model reflects reality better than the other. As stated earlier, the actual experiment is more difficult to carry out. Perhaps we should defer to NOAA...

 

[CuNanoTube]

Damn, that what I am studying in chem tomorrow.

 

[spoolin01]

Interesting foray - any idea why your VDW model produced much greater difference from ideal for air at low pressures than the Harlow chart shows? What about watboy's assertion that VDW is not a good model at higher pressures (though the Harlow chart seems to show the opposite)? Like watboy I don't follow an error claim however it's framed - the sig figs and resultant calculational precision don't support anything until the model is shown to be correct. You point out the lack of a molecular interaction term as one possible flaw... As another wrinkle, how does the SPG accuracy vary over tank pressure and is that also affected by ambient pressure and temperature? It just occurs to me too - how constant is tank volume under different fill and dive conditions? Do these aspects approach comparable effect to the ideal gas law deviation?

 

[rcs9250]

And don't forget to throw in the relative lack of accuracy of an SPG at the low end of its scale. When it gets low , tap it first to see if tapping makes the needle change positions.

 

[it_mike]

Shows what you guys know...


Any geek can tell you the answer is 42!