Compressors, Gas Turbines and Jet Engines
An ideal air compressor cycle without clearance on P-V diagram can be represented by following processes

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

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

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

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Compressors, Gas Turbines and Jet Engines
Volumetric efficiency of a compressor with clearance volume

Decreases with increase in compression ratio
Increases with increase in compression ratio
In not dependent upon compression ratio
May increase/decrease depending on compressor capacity

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