Air enters the first stage of a compressor operating at steady state at $96$ kPa, $16$oC with a volumetric flow rate of $162$ m$3/$min$.$ The compression occurs in two stages, with each stage being a polytropic process with n$=1\mathrm{.}27.$ The air is cooled to $27$oC between the compressor stages by an intercooler $($a heat exchanger$)$ operating at a constant pressure of $310$ kPa. Air exits the second stage compressor at $1$MPa.

Assuming ideal gas, determine, in kW$,$ a$.$ The power and heat transfer rate for each compressor stage

b$.$ The heat transfer rate for the intercooler