MadSci Network: Physics

Re: Why do compressed gases freeze when decompressed?

Area: Physics
Posted By: Michael Weibel, Grad student Chemistry/Physics, University of Utah
Date: Wed Jul 9 22:29:17 1997
Area of science: Physics
ID: 867954772.Ph
Hi Tim...this is a good question that has 2 answers (I think).  We can
consider a gas that when compressed is a liquid (CO2, I think) or one
that remains a gas when compressed (like helium).

For the first case, let's imagine you open up a cylinder of compressed CO2.
The CO2 goes from a liquid to a gas as it exits the cylinder (due to 
collisions with air molecules...these collisions impart energy to the CO2
"droplets", allowing them to become such, the surrounding air
has less energy and is "cooled").  This is the same thing that happens when
you get acetone (used to be a component of nail polish remover..maybe
still is?) or alcohol on your skin.  The liquid "steals" heat from your
skin and evaporates, thereby cooling the skin off.  This is also the 
principle behind the operation of your refrigerator...a Freon is sprayed
out of a small nozzle (it's a high vapor pressure liquid...which means
that it evaporates easily, much like acetone and methanol (see a connection?)
Freon collisions with the wall of a copper tube that the expansion takes 
place within remove energy, thereby cooling it.  A compressor collects
the gaseous Freon and compresses it back to a liquid..this generates heat,
which must be removed (usually by a fan).

So far so good?

expansion from a tank of helium is something that I'm not as familiar with,
but here goes...

This type of expansion is called "isentropic"...entropy (randomness) is
conserved.  If you call helium a "perfect gas"...i.e. one with no exchange
of energy between gaseous particles (clearly impossible), then you can
can combine the equations dH = TdS + VdP (Maxwell eq I think) and 
dH=Cp dT , then work through some integrals to establish that:

(T2/T1) = (P2/P1)^(R/Cp)

I think that a reasonable way to think about this is that to maintain
constant entropy (randomness), as the pressure decreases in the "system" 
(cylinder and gas), energy must leave the system as well (cooling) to 
balance the increase in entropy that you get as the pressure drops
(with a lower pressure, there is more "room" to move)...I don't expect
this cooling to be as noticeable as that for the first case because of
the exponent...if you take the ln of both sides, for a 20% decrease in
pressure (i.e. P2=.8*P1), T2 will go down by quite a bit less than 20%.

I hope that this answers your question without making it too unreadable.

Please feel free to email me if I can clarify anything or help at all.

Best Regards,
Mike Weibel

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