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Basically can engineers design a machine where , while we are freezing and compressing the air for energy storage, we can also purify it of pollutants?

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  1. Compressing air (for energy storage or other purposes) heats it up, expansion cools. For energy storage the heat has to be stored, a detailed description can be found here. Cooling air further would require additional energy input - twice, for cooling and then again for reheating upon expansion. Again, see the link for details.

  2. Compression concentrates dust etc (1g dust per 1m³ at 1bar becomes 6g/m³ at 6bar approx). It's certainly viable to have a coarse filter to protect the compressors, then a fine filter for the high pressure air. If this is what you mean by pollutants. This is farily common in compressed air systems for pneumatics: Fine filter and dewatering are installed downstream of the compressors

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So two possibilities:

One, pre filter the air prior to cooling/freezing

Two, will the impurities freeze and soldify first? If so remove solids before final freezing.

Are you freezing the air to a solid / liquid as this may make a difference.

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