Compressors, Gas Turbines and Jet Engines
The advantage of multistage compression over single stage compression is

Decreased discharge temperature
Higher volumetric efficiency
All of these
Lower power consumption per unit of air delivered

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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
The compression in both the cylinders is polytropic
There is no pressure drop in the inter-cooler
All of the listed here

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