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
All of the listed here
The suction and delivery of air takes place at constant pressure

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Compressors, Gas Turbines and Jet Engines
If p₁, is the pressure of air entering the L.P. cylinder and p₂ is the pressure of air leaving the L.P. cylinder (or inter-cooler pressure), then the ratio of cylinder diameters for a single acting, two stage reciprocating air compressor with complete intercooling is given by (where D₁ = Dia. of L.P. cylinder, and D₂ = Dia. of H.P. cylinder)

D₁/D₂ = p₂/p₁
None of these
D₁/D₂ = p₁ p₂
D₁/D₂ = p₁/p₂

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