Lunch With George!

Gas Temperature

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September 13, 2001: Gas Temperatures (revisited)

In Feynman's book Six Easy Pieces, his chapter on Atoms in Motion describes how gas in a container with a piston behaves. He demonstrates via a figure (1.3) that if the piston is slowly moved to compress the gas, the temperature of the gas will rise (see a great applet which demonstrates this concept!). Keep in mind that higher temperature = increase in motion. The reason for this result is that as gas molecules collide with the piston which is moving downward (i.e., toward the gas), the piston imparts a net gain in speed to each molecule (thus increasing the motion, and therefore the temperature, of the molecule and the gas as a whole).
If I haven't been very clear, then you better get a copy of the book! Feynman does it much better.
(By the way, the converse is also true-- if you pull the piston away from the gas, the gas will become cooler for the same reason-- when a molecule of the gas collides with the piston moving away, the speed of the piston must be subtracted from the speed of the molecule.)

[This material has all been a review of what George and I talked about several lunches ago, when we first began reading the Feynman book. I've provided this as a background for George's topic today!]
On with the story...

George was telling me that in an air-conditioning system (or, I suppose, any refrigeration system), a gas is contained in a chamber, but some of the molecules escape (are pushed???) through a VERY tiny opening into a larger chamber, where the pressure is much lower. I assumed when he was telling me all this that the second chamber must get pretty cold and that's what is used to cool stuff down (air, etc.).
George points out that even though the molecule has escaped into a lower-pressure chamber, it should still be moving at the same speed. that means the same energy, and the same temperature. So how does it get cold???
I mentioned a great two-volume set of books called The Way Things Work by C. Van Amerongen, thinking that a deciption of a refrigeration system might be found there... but George correctly pointed out that these books (which, it turns out, he owned when he was but a lad) most likely only describe how it works mechanically, paying no mind to the underlying physics. Bummer. They're great books, though! Here's a testimonial by at least one of my favorite authors: Long after I had purchased my copies, I was reading Lucifer's Hammer, by Larry Niven & Jerry Pournelle. After a comet strikes the Earth, an aging science professor is forced to leave his home and can only save a handful of the books from his extensive personal library... and he makes sure that volumes 1 and 2 of The Way Things Work are among them!
Oops... I digress... back to the Gas Temperature story:
The bottom line: We Don't know! I guess we better look this up somewhere. If anyone else knows, please send e-mail!
September 16, 2001: E-mail from Fred

Hi Paul,
I shall attempt to explain mechanical refrigeration, maybe it will answer your question.
A mechanical refrigeration consists of the following:
1. a compressor, a device to compress gas
2. a condenser, a coil with a fan blowing air across it
3. a expansion valve, a device that restricts the flow of liquid
4. and an evaporator, a coil with a fan blowing air across it.
So connect this together so that you have the output of the compressor connected to the condenser, then to the expansion valve, then to the evaporator and then back to the compressor.
Start the cycle by the compressor delivers gas at high temperature and pressure to the condenser. Heat is removed (from the condenser) by blowing air across the condenser, resulting in condensation of the gas to a liquid, still under high pressure. The liquid passes through the expansion valve emerging as a mixture of liquid and vapor at a much lower temperature. Heat is added (to the evaporator) by blowing air over the evaporator and the remaining liquid changes into vapor. This warm gas returns to the compressor to start the cycle over.
It is the state changes of the coolant that makes all of this work. Compressing the warm low-pressure gas back to a high-pressure liquid and then allowing it to evaporate (low pressure liquid changes to low pressure gas) creates the cooling.
October 13, 2001: E-mail from George

Hi Paul -
I was doing some web searches to try and find out more about gas pressure and temperature, and ran across this site of physics applets: http://www98.phys.virginia.edu/classes/109N/more_stuff/Applets/home.html
In particular, this one demonstrates Feynman's explanation of the temperature rise when a gas is compressed by a slow-moving piston:

Last modified 10/15/2001.

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