Compressors, Gas Turbines and Jet Engines
An ideal air compressor cycle without clearance on P-V diagram can be represented by following processes

One adiabatic, two isobaric, and one constant volume
One adiabatic, one isobaric and two constant volumes
Two adiabatic, one isobaric and one constant volume
Two adiabatic and two isobaric

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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
Isentropic power to the power required to drive the compressor
Isothermal power to the shaft power or B.P. of the motor or engine required to drive the compressor
Volume of free air delivery per stroke to the swept volume of the piston

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

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