Excercise for you physics boffins.
In my new hobby gig as a hose-dragger, I've been practicing SCBA drills. We've been changing bottles in the dark or with a blinder mask on, donning and doffing at speed, going through obstacle courses with wax paper in our mask plates, etc. At the end of each exercises, you go to the compressor and refill the tanks. This is a fairly straightforward process, but one can't just dump the air from the waiting storage tanks in all at once, or the SCBA tanks get hot, and the air doesn't seem to want to go in. I mentioned the issue of the liquid boiling up, and one of the younger firefighters said, "liquid? It's just air. There's no liquid." I tried to explain that, thanks to Charles' Law (and Boyle's Law), gases under enough pressure do go to liquid state*, but he didn't get it.
We use the Scott air packs with carbon fibre tanks, and I hadn't realized just how awesome they were until we did some training with a neighboring agency that uses old Scott air packs with old steel tanks. The carbon fibre tanks are slightly larger than a 3-litre bottle in diameter, and a bit longer. They are filled to 4500 psi. The steel tanks are much larger --about 11" in diameter and a few inches longer-- and weigh about 4 times more. The steel tanks only go to 2500 psi. Here's the thing: both hold 45 cubic feet of air.
Interestingly, both packs will take each others' bottles, but the more modern carbon fibre bottles have to be bled down to 2500psi before being put on the older packs. Better than nothing, but not good. Given the decreased volume, 2500 psi on one of those is not much.
Supposedly, 45'^3 of air is good for thirty minutes. In my experience, I get about 10 to 15 when laboring. Hey, I'm a big boy.
While refilling the carbon fibre bottles, the same young guy gets really frustrated at how very long it takes to get from 3800 psi to 4000psi, which we've set as the minimum amount that the bottles must be filled. The large electric compressor labors for a long time, long after the storage bottles are depleted.
I told him that I am quite sure that the mass of air stacks with the volume-- it's not a linear progression for amount of air inserted for a given volume over a given time from 2500 to 2700psi, say, as it is to 3800 to 4000 psi.
So here is my question, and Stingray, take note:
For a given cylinder of, say: 6" X 21", what is the amount of volume of air (at STP) being inserted between between 2500 psi and 2700 psi?
Then, what's the volume of air (at STP) being inserted between 4000 psi and 4200 psi?
Express your answer in equivalent cubic feet, at STP.
*EDIT: Though, probably not in this case. Consensus seems to be that the pressure isn't high enough to achieve liquid air, in these bottles.