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

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

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Compressors, Gas Turbines and Jet Engines
The compressor capacity is defined as the

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

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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

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

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