Let’s say you’ve got one of these, and you’re dusting off your computer:
As you spray, you’ll notice the can getting cold. You’ve probably noticed this in similar contexts: propane tanks getting cold, helium tanks getting cold, compressed air tanks running pneumatic tools getting cold, etc. It seems that when air escapes from an enclosure, it gets cold. Well, there’s a reason.
Imagine if you will a elementary school gymnasium filled with kids and adults. The principle of the school announces free ice cream in the field outside of the gym and flings the doors open. The kids will of course freak out and run at top speed toward the desert. The adults will follow, but being afraid to look undignified they’ll saunter at a much lower speed. As a result, the rate of effusion of the fast-moving kids is higher than the rate of effusion of the slow-moving adults. As a function of time the number of kids and adults in the gym will decrease, but the ratio of adults to kids will increase. The kids are leaving faster and the thus though there are fewer of both groups, there’s proportionally a lot fewer kids.
So if you have a cylinder full of randomly-moving gas molecules, it stands to reason that the ones that happen to be faster-moving will escape an opening at a greater rate. I’ll prove it in a future post, but it will turn out that if the average kinetic energy of an escaping particle will be 1.333… times greater than the average kinetic energy of the remaining gas. And temperature is effectively just a measure of the average kinetic energy of the molecules in question, so if the average speed of the gas molecules is going down, so is the temperature. Voila! Cold!
The situation with the compressed air can is complicated somewhat by the fact that it’s not really just a gas inside. It’s a fast-evaporating liquid, which means there’s a phase transition happening as well. This adds some very difficult math from a formal statistical mechanics perspective, but the overall concept remains essentially similar.
I think it’s pretty cool. *rimshot*