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From: "JUHA FLINKMAN" <flinkman@fi*.fi*>
To: techdiver@terra.net
Date: Wed, 25 Sep 1996 15:31:07 +0200
Subject: compressibility of air
Hi everyone,

And here's the date I've promised. The compressibility of air-graph 
is in .jpg format, I hope that's not a problem to anybody.

General equation for gas volume is pV/T=constant. In this p=pressure, 
V=volume, and T=temperature. Using this equation, we can see that in 
when a 300 bar tank is filled, and the temperature rises to let's say 
47 deg C, the pressure reduces 37 bars when the tank is cooled down 
to 7 deg C in sea-water. This alone does not explain the rapid 
pressure decrease in a 300 bar tank. The formula p=V/T only applies 
to ideal gas. Real gases seldom agree to this in pressures in excess 
of 100 bars. For air, the easiest thing to do is to use 
compressibility factor Z from tables (see Sten's post and figure with 
this post). Z=pV/nRT, i.e. Z measures the deviation of the gas from 
ideal. Instead of pV/T=constant, we must use pV/TZ=constant.

For air, |Z-1| <0.02 when the pressure is <200 bar and temp <10 deg. 
C. But when p>330 bar, and T>47 deg. C, Z=1.14, making the deviation 
14% from ideal. This is well worth taking into consideration. Another 
example:

10 litre tank filled to 200 and 300 bar:

V(1)= 200 bar*10L*1.00/1.10*1bar=1980 L
V(2)=300 bar*10L*1.00/1.01*1 bar=2730 L

So, adding the last 100 bars does not add 1000 litres of air, but 
only 750L. That's why the gas goes so fast in the beginnig of the 
dive.

I'm a marine biologist, and as said, learned all this from my 
engineer buddies, especially Matti Leinio and Pekka Raty. I'll try to 
persuade them to put more of this stuff on the techdiver, if 
anybody's interested. Matti (a medical physics engineer and trimix 
diver) says that with helium, the compressibility factor is even bigger 
issue than with air. Anyway, I hope you guys find this useful.

Good dives,
Juha 

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