Compressors, Gas Turbines and Jet Engines
The assumption made in two stage compression with inter-cooler is that

The suction and delivery of air takes place at constant pressure
There is no pressure drop in the inter-cooler
All of the listed here
The compression in both the cylinders is polytropic

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Compressors, Gas Turbines and Jet Engines
In the axial flow gas turbine, the work ratio is the ratio of

Output and input
Actual total head temperature drop to the isentropic total head drop from total head inlet to static head outlet
Actual compressor work and theoretical compressor work
Compressor work and turbine work

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

Volume of free air delivery per stroke to the swept volume of the piston
Work required to compress the air isothermally to the actual work required to compress the air for the same pressure ratio
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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