What is the easiest and cheapest way to create liquid oxygen?



Answer:
Liquid oxygen is prepared by submersing a copper coil into liquid nitrogen and blowing oxygen through it from an oxygen tank . It is paramagnetic when in the field of a strong magnet.
You have to either put it under tremendous pressure or intense cold. Nothing that you are capable of doing or purchasing, however, I'm afraid.
This involves extreme cold but I think it is the cheapest and easiest way:

Manufacture from liquefied air

Oxygen may be obtained from the atmosphere by the liquefaction and fractional distillation of air. Liquid air is a mixture of liquid nitrogen, boiling point -196 degC, and liquid oxygen, boiling point -183 degC. The nitrogen is more volatile (i.e. it has a lower boiling point) and boils off first during evaporation. Because some oxygen evaporates with the nitrogen, separation of the two gases is brought about by fractionation (i.e. by letting the evolved gas mixture bubble through liquid air rich in oxygen in a tall rectifying column). The oxygen in the gas mixture condenses and almost pure nitrogen gas leaves the top of the column, leaving almost pure liquid oxygen which is then evaporated to give oxygen gas. The oxygen gas is distributed as a compressed gas in high pressure cylinders.

ref: http://www.ucc.ie/academic/chem/dolchem/...
There is no easy or cheap way to liquefy Oxygen.
It is separated from the components of liquid air by distillation.
The process involves compression to high pressure (the Critical pressure) and cooling to the critical Temperature.
This is done by a series of compression, cooling, expansion, re-compression, more cooling and expansion processes into a chamber where the final expansion produces liquefaction.

Once in liquid form, the oxygen can be stored at just above atmospheric pressure in a 'Dewar' type vessel (like a vacuum flask).

Critical temperature, = -118.38°C.
Critical Pressure = 50 atm.
The gas will not condense if either of the two above conditions is not met.
Boiling point at 1 atm = -182.96°C.
LOX is some dangerous stuff. Not a good idea to put the directions for making it on a public forum. Or asking for the directions for that matter.

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