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Using liquefaction of gases to make an habitable dome

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Liquefaction of gases is physical conversion of a gas into a liquid state (condensation).

I found that liquefaction is used to get liquid air and then split it into liquid compounds O2, N2, CO2, etc (each gas has its own boiling and melting points and density which can be used to split them).

Imagine a world with an atmospheric pressure of, I don't know... 45 kPa made of 90% N2 and 10% O2, so:

$$ \left| \begin{array}{cc|ccc|c} \text{Gas}&\text{%}&\text{gr/mol}&\text{Mols}&\text{Fractal Mol}&\text{Partial Pressure (kPa)}\\ \text{O2}&\text{10%}&31.99&0.31&\text{8.86%}&3.98\\ \text{N2}&\text{90%}&28.01&3.21&\text{91.13%}&41.01\\ \text{Total}&\text{100%}&60.01&3.16&\text{100%}&45 \end{array} \right| $$

  • O2 10%: 3.98 kPa partial pressure. Hypoxia, in this answer I explain it.
  • N2 90%: 41.10 kPa partial pressure. Nothing bad, in this answer I explain it (and about hypoxia).

Atmophere in this $X$ planet is about 45 kPa, our atmosphere is 101.325 kPa but at 45 kPa we don't die (or at least I think we won't die and water will boil at 41.32 °C (How to calculate it)), the only problem here is the O2 value.

To survive in this planet we could do these 2 ideas:

  • Build domes: We can live in sealed domes where we have machines that make liquefied air and extract the liquid oxygen at 3.98 kPa from the atmosphere and inject it into our dome at 1 atm (21 kPa O2 PP and the rest of N2). This way we don't have to make our own oxygen from water or plants.
    My question is if it's possible to make that machine to "condense" the oxygen from the atmosphere and infuse to our dome constantly (never stopping, otherwise we would die). Obviously this machine would have an emergency power supply.
  • Have a pocket liquefaction personal machine: My other idea is make personal and portable liquefaction machines for each person to concentrate the O2 PP from the air each time they take a breath. My question is if it's possible to make such small and portable machine for each person. Maybe it could be like a backpack with inner batteries.
    Obviously this second idea can be replaced with a simple tank, in the base colonists could recharge their breathing tanks.

Please I don't want "Yes, it could be possible.", I want some explanation behind answers.

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This post was sourced from https://worldbuilding.stackexchange.com/q/84446. It is licensed under CC BY-SA 3.0.

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