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
The compression in both the cylinders is polytropic
There is no pressure drop in the inter-cooler
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

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

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