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

Isentropic power to the power required to drive the compressor
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

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Compressors, Gas Turbines and Jet Engines
The following is true for an open cycle gas turbine having exhaust heat exchanger. Atmospheric air before entering the compressor is

Compressed air before entering the combustion chamber is heated
Heated
Bled gas from turbine is heated and readmitted for complete expansion
Exhaust gases drive the compressor

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