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I would like to find out how much energy is required to liquify gases (oxygen or nitrogen, for example). What are some relevant equations?

I'm curious whether creating small quantities of dry ice or cryogenic fluids is feasible at home. If James Dewar was able to liquify hydrogen in 1898 surely it must not be that difficult!

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You might take a minute to contemplate the construction of a vacuum flask (AKA "dewer"). These guys weren't amateurs, they had time, money, and access to sophisticated equipment. Dry ice should be feasible, and liquified gasses might be, but you're going to need more than a few equations to manage it. –  dmckee Mar 23 '11 at 4:11
    
Many things that were once restricted to professionals are now accessible to hobbyists. I am trying to get a sense of whether cryogenics is one of them. At the very least, humor my curiosity and treat the question as a thought experiment! –  M. Dudley Mar 23 '11 at 5:07
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I'm always happy to hear about another hobbyist. However, be aware that high-pressure gases are incredibly dangerous. Let me say that again: High pressure gas is incredibly dangerous. In grad school I was almost killed by a small 800 psi argon explosion. Even a small volume of liquid nitrogen in a sealed soda bottle will explode with enough force to take your fingers. –  Andrew Mar 23 '11 at 16:39
    
A primary source for those links: ucih.ucdavis.edu/docs/chemistry_301a.pdf –  Andrew Mar 23 '11 at 16:45
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1 Answer

This question first requires some "sorting".

  • As long as You want to do that with nitrogen or oxygen, so called "permanent gases" in this context, the answer is no. Linde machines are plants! The first liquefied air was made in lab (Krakau) with simpler apparatus, but nevertheless I doubt You could tinker something like that, high pressures and precooling to rather deep temperatures are necessary.

  • If You content with "not permanent" gases, then just take a flask for refill of lighters (Butane) and open the nozzle pointing it down into a glass. some liquid and cold and boiling butane will collect.

  • "dry" ice is simple too, just take a fire extinguisher filled with liquid carbon dioxide and open the nozzle and blow into a bag made from coarse linen. Dry ice (snow) will collect in the bag. Depending on inner construction of the gas cylinder (raiser or not) You have to hold it upside down maybe. In general do the way prescribed for the extinguisher in use.

Edit, I forgot Your asking for "equations". Look for "Joule-Thompson-effect" (Wikipedia) the only thing You will need, is the inversion temperature. Calculations maybe will show You the difficulty to make liquid air.

Edit/PS

If You try to tinker in this domain, please be aware that steel (and other metals) will be very brittle at liquefied air temperatures.(Danger of explosions) Selection of materials is a very important part of cryogenics.

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