Compressors, Gas Turbines and Jet Engines
In air compressors, free air delivery means the

Volume of air sucked by the compressor during its suction stroke
Volume of air delivered by the compressor
None of the listed here
Actual volume of the air delivered by the compressor when reduced to normal temperature and pressure conditions

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Compressors, Gas Turbines and Jet Engines
The assumption made in two stage compression with inter-cooler is that

The compression in both the cylinders is polytropic
All of the listed here
There is no pressure drop in the inter-cooler
The suction and delivery of air takes place at constant pressure

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