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I should say it is closer to Isothermal process when the air in a compressor is cooled in between stages (Of course for multi stage compressor).

The cooling brings the work from Adabatic process towards the isothermal process (constant temperature) which increases the efficiency.

for more info, check-http://www.marineinsight.com/tech/auxiliary-machinery/efficiency-of-air-compressor-and-uses-of-compressed-air-on-a-ship/

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