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

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Compressors, Gas Turbines and Jet Engines
The following is true for an open cycle gas turbine having exhaust heat exchanger. Atmospheric air before entering the compressor is

Heated
Compressed air before entering the combustion chamber is heated
Exhaust gases drive the compressor
Bled gas from turbine is heated and readmitted for complete expansion

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