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

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Compressors, Gas Turbines and Jet Engines
Volumetric efficiency of a compressor without clearance volume

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

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Compressors, Gas Turbines and Jet Engines
If p₁ is the pressure of air entering the L.P, cylinder and p₃ is the pressure of air leaving the H.P. cylinder, then the ratio of cylinder diameters for a single acting, two stage reciprocating compressor with complete intercooling is given by

D₁/D₂ = (p₁ p₃)1/2
D₁/D₂ = (p₁/p₃)1/4
D₁/D₂ = (p₁ p₃)1/4
D₁/D₂ = (p₃/p₁)1/4

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