Compressors, Gas Turbines and Jet Engines
The advantage of multistage compression over single stage compression is

Higher volumetric efficiency
All of these
Decreased discharge temperature
Lower power consumption per unit of air delivered

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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
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

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