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

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

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Compressors, Gas Turbines and Jet Engines
In a turbo jet engine, subsequent to heat addition to compressed air, to get the power output, the working substance is expanded in

Turbine blades, which is essentially an isentropic process
Exit nozzle, which is a constant volume process
Exit nozzle, which is essentially an isentropic process
Turbine blades, which is a constant volume process

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Compressors, Gas Turbines and Jet Engines
Water gas is produced by

Passing air and a large amount of steam over waste coal at about 65°C
Partial combustion of coal, eke, anthracite coal or charcoal in a mixed air steam blast
Carbonisation of coal
Passing steam over incandescent coke

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