Learn more physics!
From reviewing your response about making liquid nitrogen, it is not clear to me, why passing compressed air over coils causes it to liquify. Are these coils special? What type of coil is used? If compressing air causes it to liquify, what other steps are involved in separating the various gases?
You're right that the old answer went by kind of fast. Here's the idea again.
When you compress some air, you're putting energy in and it heats
up. You can get it back to room temperature just by running it through
some coils which aren't special, they just have a lot of surface area
to let heat flow out to the room. Now if you let that compressed gas
expand again, it does work, loses energy, and gets cold.
You can chain a few stages like that together. For example, the
compressed air in the second stage can run through coild immersed in
the cold air from the first stage. It then starts off cold and gets
even colder when it expands.
I think the gases are separated by using the tendency of some to
evaporate more easily than others from the liquid, but I'm not sure.
(published on 10/22/2007)
Follow-up on this answer.