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

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

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

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

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