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Oxygen and nitrogen can be liquified by compressing them, allowing them to cool to room temperature, then allowing them to re-expand (which chills them further due to the Joule-Thompson effect) and using the chilled gas to further cool the compressed gas. By repeating this cycle eventually the gas will drop below its boiling point and liquify.

In practice, since oxygen boils at a higher temperature than nitrogen and liquid nitrogen is easy and relatively cheap to obtain, small amounts of liquid oxygen for lab use are generally prepared by allowing oxygen gas from a cylinder to flow through a coil submerged in liquid nitrogen.

Helium is much more complicated, since it exhibits a negative Joule-Thompson effect at room temperature (it actually gets warmer upon expansion). It must be chilled down below about 50 K before it can be cooled further by expansion (and, since liquid nitrogen boils at about 77 K, you can't use liquid nitrogen to get gaseous helium cold enough to even start the Joule-Thompson process).

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