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

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Compressors, Gas Turbines and Jet Engines
The overall isothermal efficiency of compressor is defined as the ratio of

Power to drive compressor to isothermal h.p.
Isothermal h.p. to adiabatic h.p.
Work to compress air isothermally to work for actual compression
Isothermal h.p. to the BHP of motor

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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
The suction and delivery of air takes place at constant pressure
There is no pressure drop in the inter-cooler

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