Compressors, Gas Turbines and Jet Engines
In a turbo jet engine, subsequent to heat addition to compressed air, to get the power output, the working substance is expanded in

Turbine blades, which is essentially an isentropic process
Exit nozzle, which is essentially an isentropic process
Turbine blades, which is a constant volume process
Exit nozzle, which is a constant volume process

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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)/2
p₂ = Pa p₃/p₁
p₂ = p₁. p₃

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