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

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

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Compressors, Gas Turbines and Jet Engines
An ideal air compressor cycle with clearance on P-V diagram can be represented by following processes

One adiabatic, two isobaric, and one constant volume
Two adiabatic, one isobaric and one constant volume
One adiabatic, one isobaric and two constant volumes
Two adiabatic and two isobaric

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

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

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