Compressors, Gas Turbines and Jet Engines
Inter-cooling in multistage compressors is done

To enable compression in two stages
To cool the air during compression
To cool the air at delivery
To minimize the work of compression

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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

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

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Compressors, Gas Turbines and Jet Engines
For minimum work in multistage compression, assuming same index of compression in all stages

Work done in all stages should be equal
Work done in subsequent stages should increase
Work done in subsequent stages should decrease
Work done in first stage should be more

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