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

Isothermal h.p. to the BHP of motor
Isothermal h.p. to adiabatic h.p.
Work to compress air isothermally to work for actual compression
Power to drive compressor to isothermal h.p.

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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
Exhaust gases drive the compressor
Bled gas from turbine is heated and readmitted for complete expansion

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