From: wolgamot@milton.u.washington.edu (Greg Wolgamot)
Newsgroups: rec.scuba
Subject: Re: Tank thermal (de)compression question
Date: 13 Aug 92 19:23:09 GMT
Organization: University of Washington, Seattle

In article <1992Aug12.230515.8338@ultb.isc.rit.edu> awpsys@ritvax.isc.rit.edu writes:
>In article <1992Aug11.144334.3439@engage.pko.dec.com>, zipp@foosw6.enet.dec.com (Eric S. Zipp) writes:
>>Greetings,
>>
>>	Ok all you bubble blowing physicists, refresh my memory with a bit
>>of basic physics 101.
>>
>>	Upon compressing air in a tank, the process results in the generation
>>of a good bit of heat (which is why the tanks are immersed in water during
>>the process).
>>
>>	Upon venting a volume of air from the tank, the first stage, becomes
>>quite cool(cold).
>>
>>	What exactly is generating/absorbing the heat during these processes?
>>
>>Inquiring minds want to know... ;-)
>>
>>Thanks,
>>
>>Eric 
>>
>
>Simple physics.   PV=nrT is the gas law in question.
>
>	P = pressure
>	V = volume
>	T = Temp
>
>	n and r are constants that escape me for now but are not needed for
>	this discussion.
>
>	solving = for T
>
>		T = PV/nr
>
>	T will rise when we raise pressure and drop when you drop pressure.
>	(assuming volume does not change...which we hope for with our
>	tanks :) )
>
>	This is how refrigerators work as well.  and chinook winds 
>
>- Andy
>
>	

   I think the ideal gas law explanation is a little too simple of
physics to accurately describe the system.  While I agree that the
value of the gas constant R does not matter, the "constant" n is or
is not a constant.  n is the number of moles of gas, so if your
system is the air inside the tank, n increases as the tank is filled.
This increase in n masks the effect of pressure on the temperature.
  I think the First Law of Thermodynamics does a little better job
describing the system.  As I will hopefully describe, the increase
in temperature during filling comes from the work done on the gas
by the air compressor, and the decrease in temperature during the
release of pressure comes from the air needing to push back the
atmosphere (which takes energy).  Clear as an algae bloom?
  The First Law: dU = dq + dw.
  The variables:
	dU is the change of internal energy of the system.  When dU
increases, the temperature goes up (I'm simplifying this way too much,
probably.  By hey! I'm only a first year grad student!)
	dq is the change of heat energy, with a positive value 
corresponding to an increase in energy by the system. Note: a positive
dq DOES NOT mean that the temperature rises; temperature change is a
measure of dU.
	dw is the work term.  In this case, the work being done on the 
system in filling is by the air compressor (a positive dw).  The
work being done in emptying the tank by the air is done on the atmosphere,
because the expanding air has to "push back" a pocket in the atmosphere
so it has a place to occupy.  This corresponds to a negative dw, 
because the work is done BY the system.
	Now let's tie this together. First, we fill the tank.  dw is 
very positive, because the compressor is doing work on the gas by
compressing it.  dq is slightly negative as the warming air warms
the tank surrounding it.  If we consider the tank to be filled very
quickly, the air would not have time to warm the aluminum tank,
and so dq = 0, which would be adiabatic.)  Since dw is very positive,
and dq is slightly negative, or in an ideal case zero, the resulting
dU from the First Law is positive.  Hence, the internal energy has
increased, as measured by the air (and the tank in contact with the air)
warming up.
	Now we empty the tank.  dw is now very negative, because the
expanding air has to do work on the atmosphere by pushing it back.
Again, dq is zero in an ideal, fast situation.  More realistically,
dq is slightly positive, as the air pulls heat from the aluminum walls
of the tank.  Using the equation above, we see that dU is negative.
Hence, the internal energy of the air has decreased, and we can see
this because the air has gotten colder.
	I'm sure a person studying thermodynamics would shiver if
he read this explanation, but I think it's not too far off, if we
consider the situation fairly ideal, and our audience fairly gullible!
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