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
All of the listed here
The compression in both the cylinders is polytropic

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

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Compressors, Gas Turbines and Jet Engines
Ratio of compression is the ratio of

Gauge discharge pressure to the gauge intake pressure
Stroke volume and clearance volume
Pressures at discharge and suction corresponding to same temperature
Absolute discharge pressure to the absolute intake pressure

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