pressure/volume question

[dc4bs]

Hi all,

Given constant volume and temperature, is the pressure vs. compressed volume equation linear or a curve?

For example:

A 'standard' 80 ft3 Aluminium scuba cylinder at operating pressure of 3000 lbs/ft3 contains roughly the equivalent of 80 ft3 of gas at 1 Atm

The same cylinder at 1500 lbs/ft3 has how much gas at 1atm equivalent?

If it is a linear equation, it would be about 40 ft3.

If it's a curve, can someone point me to a formula, or better yet, a souce where I can get to understand the pressure, static container volume, compressed gas volume relationship better?

[Groundhog246]

The FIRST gas law we studied, the first night of our OW course was BOYLES LAW. If you double the pressure on a gas you half the volume. Therefore if you half the pressure you double the volume. Therefore it's linear and a tank that holds the 1ATM equivalent of 80ft3 at 3000psi holds 40ft3 at 1500psi.
It's also why the rule of thirds works. If it was non linear we'd have to carry some kind of graph in order to have useful info from our spg.
It's nice to get a nice simple "law" now and then.

:jester:

[Munin]

Groundhog246 once bubbled...
The FIRST gas law we studied, the first night of our OW course was BOYLES LAW. If you double the pressure on a gas you half the volume. Therefore if you half the pressure you double the volume. Therefore it's linear and a tank that holds the 1ATM equivalent of 80ft3 at 3000psi holds 40ft3 at 1500psi.
It's also why the rule of thirds works. If it was non linear we'd have to carry some kind of graph in order to have useful info from our spg.
It's nice to get a nice simple "law" now and then

That is the IDEAL gas laws. Volume decreases as pressure increases. Past 3000 psi or so the volume loss is more dramatic. 3500 is not 1/6 more than 3000, 4000 is not 1/3 more than 1000. The difference is not particularly significant, but it does exist and is more noticeable with helium, which compresses more than air or oxygen.

Try this for an explanation (http://www.combro.co.uk/nigelh/diver/vdw.html) and this for more. (http://www.atomox.net/)

Sorry, not so simple. :(

[Rick Murchison]

dc4bs once bubbled...
Given constant volume and temperature, is the pressure vs. compressed volume equation linear or a curve?

Is a perfectly level road straight, or does it have a curve to it? Well, it's curved - with the curvature of the earth, but not so's it'd make a difference you'd notice in everyday use.
And so it is with air or Nitrox at recreational pressures - there's a bit of a curve there, but not enough to fret with.
Rick

[cpalerm]

Groundhog246 once bubbled...
BOYLES LAW. If you double the pressure on a gas you half the volume. Therefore if you half the pressure you double the volume.


You are right in that the relationship is linear, but Boyle's Law is not the correct explanation. Boyle's Law is for the same amount of gas (mass is constant).
If you look at the full relationship for (ideal) gases, one expression is:
Pressure = R * density * Temperature
where R is a constant that depends on the gas, and the density is the mass divided by the volume.
If you are interested in more details, here is a link to a very good and simple explanation

http://www.grc.nasa.gov/WWW/K-12/airplane/eqstat.html

Cesar

[padiscubapro]

Munin once bubbled...


That is the IDEAL gas laws. Volume decreases as pressure increases. Past 3000 psi or so the volume loss is more dramatic. 3500 is not 1/6 more than 3000, 4000 is not 1/3 more than 1000. The difference is not particularly significant, but it does exist and is more noticeable with helium, which compresses more than air or oxygen.

Try this for an explanation (http://www.combro.co.uk/nigelh/diver/vdw.html) and this for more. (http://www.atomox.net/)

Sorry, not so simple. :(

Helium's compressibilty factor is higher meaning its LESS compressable.. The "compressability" factor is used as a divisor.

Thats why when you see stated compacity of industiral cylinders, the rated capacity of an oxygen cylinder is greater than that of a helium cylinder even though the use the same cylinder(different valve).

[omar]

It actually depends on the temperature, volume of the container, and the gas. For a graph of air, helium and oxygen compressibility see:
http://www.atomox.com/gas_graph.html

Note: An ideal gas would follow a value of 1.0 at all pressures. These were done for a unit volume. If the volume of the container is reduced the interaction of the molecules becomes more pronouced and the the compressibility will change more.

The compressability values for the common scuba gases are at:
http://www.atomox.com/Z_factor.html

Do a search for real gas EOS (equation of state) such as Redlich-Kwong, Beattie-Bridgeman, etc etc. There are about a dozen in "common" use, and alot more that are used but obscure.

omar

[dc4bs]

I kinda figured linear would be too simple.

The whole reason for the question was because my LDS is currently pushing steel LP 45s for stage / deco bottles and my budy and I don't want steel.

The LDS doesn't want to have to deal with trying to fill higher O2 content to 3000 lbs (would prefer 2400 in the LPs).

We don't want to deal with extra negative bouyancy and rust issues.

I was thinking that rather than a steel 45, an AL 50 (luxfer 48.4@3000) filled to 2400 might be doable.

That would give us 38.72 ft3 using linear math and, in theory, the curve is in our favor in this case...

It would start out slightly more negativly bouyant than a full AL40 (still less than a S45) but be less positively bouyant when empty (due to larger cylinder).

The only drawback I can see is a slightly shorter, wider, less streamlined bottle... I've used a 65 as a deco bottle before so I dont think it'll be all that bad.

I'd appreciate any further ideas or comments from everyone on this. Tell me why this is a bad idea if it is and there's someting important I havn't thought of yet.

Thanks,
Craig

NOTE: bottle info taken from Luxfers website
http://www.luxfercylinders.com/americas/product_info/scuba/specifications.htfx.htm

[patmandu]

The LDS doesn't want to have to deal with trying to fill higher O2 content to 3000 lbs (would prefer 2400 in the LPs).


Just curious, why do you need the extra O2 that you would gain by boosting the AL40 to 3000psi?

Seeing that you use the 02 from 20fsw/ffw to the surface, your consumption won't be too bad (as compared with breathing the bottle at a deeper depth where obviously the gas would be consumed 'faster'). If you require more gas, what about just using an AL80 (good bouyancy characteristics) and filling to 2000psi or whatever you can fill to from a fresh cylinder if cascading.

For ocean deco diving, we use an AL40 or AL80 for the deeper deco gas and an AL40 for O2 which we routinely get at least 2 dives off of (of course these are weenie deco dives with less than 40 minutes or so of deco).

Just curious.

--Pat

[Munin]

I agree, you really shouldn't need the full pressure in an Al40. I get more than two dives worth of O2 with a 40 or even a 30 at 23-2400 psi on dives with < 90 minute runtimes in the ocean. If you're diving mix a single 40 of 50% works well on a single dive and will even be adequate for two shorter dives. As for buoyancy, stay very, very far away from steels. My 30s with a DS4 are a little bit negative when dead empty, the 40s are a tad positive. IOW, enough capacity and perfect buoyancy.

[dc4bs]

See, that's why I ask questions.

So I can find out where my thinking is wrong. I dunno why I let myself get locked onto the idea of an arbitrary number like 40 ft3 as a 'must have'. :rolleyes:

I gotta go back and rework the problem from the angle of 'exactly what do I need for the diving I'm doing' and go from there. :)

Looks like I'll be getting the AL 40's after all.

Thanks for the input guys.

[AquaTec]

dc4bs once bubbled...
Hi all,

Given constant volume and temperature, is the pressure vs. compressed volume equation linear or a curve?

For example:

A 'standard' 80 ft3 Aluminium scuba cylinder at operating pressure of 3000 lbs/ft3 contains roughly the equivalent of 80 ft3 of gas at 1 Atm

The same cylinder at 1500 lbs/ft3 has how much gas at 1atm equivalent?

If it is a linear equation, it would be about 40 ft3.

If it's a curve, can someone point me to a formula, or better yet, a souce where I can get to understand the pressure, static container volume, compressed gas volume relationship better?




Air inside a closed cylinder is not subject to Boyals law as the ata do not change. so in your formula, a tank the contains 80 cu/ft at 3000 psi when filled to 1500 psi would be 50% full therefor it would contain 40 cu/ft.

the air is not subjet to the pressures outside the tank.

mind you the gas law that has to due with temprature change does apply, if you leave that 1500 psi tank in the sun and the temprature rises i beleive that the formula is 1 psi per 1 degree ferenhiet in temp difference. therefor the cu/ft would also change porportionaltly


now if the tank was a flexible one say a balloon the or other closed flexable container then the veriouse gas lawas would apply