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 = p₃/p₁
p₂ = p₁ × p₃

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

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

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

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

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