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

Work required to compress the air isothermally to the actual work required to compress the air for the same pressure ratio
Volume of free air delivery per stroke to the swept volume of the piston
Isothermal power to the shaft power or B.P. of the motor or engine required to drive the compressor
Isentropic power to the power required to drive the compressor

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

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