Compressors, Gas Turbines and Jet Engines
The inter-cooler pressure, for minimum work required, for a two stage reciprocating air compressor, is given by (where p₁ = Intake pressure of air, p₂ = Inter-cooler pressure, and p₃ = Delivery pressure of air)

p₂ = p₁/p₃
p₂ = p₃/p₁
p₂ = p₁ × p₃
p₂ = p₁ × p₂

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

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

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