Compressors, Gas Turbines and Jet Engines
For a two stage reciprocating compressor, compression from p₁ to p₃ is with perfect intercooling and no pressure losses. If compression in both the cylinders follows the same polytropic process and the atmospheric pressure is pa, then the intermediate pressure p₂ is given by

p₂ = Pa p₃/p₁
p₂ = p₁. p₃
p₂ = (p₁ + p₃)/2
P₂ = Pa × p₃/p₁

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Compressors, Gas Turbines and Jet Engines
In the axial flow gas turbine, the work ratio is the ratio of

Output and input
Compressor work and turbine work
Actual compressor work and theoretical compressor work
Actual total head temperature drop to the isentropic total head drop from total head inlet to static head outlet

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

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

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