A two$-$stage, double$-$acting, reciprocating air compressor operating at $300$ rpm receives air at $1$ bar and $27$C$.$ The bore of the LP cylinder is $360$ mm and its stroke is $400$ mm$.$ Both cylinders have equal stroke and equal clearance of $4\%.$ The LP cylinder discharges air at a pressure of $5$ bar. The air then passes through an intercooler to cool air to its initial temperature. Pressure drops in the intercooler to $4\mathrm{.}75$ kPa. Finally, air is discharged from the HP cylinder at $15$ bar. The index of compression and expansion in both cylinders is $1\mathrm{.}3.$ Cp $=1\mathrm{.}005$ kJ$/$kg$-$K$,$ and R $=0\mathrm{.}287$ kJ$/$kg$-$K$.$

Calculate:

$($a$)$ Heat rejected in the intercooler, $($b$)$ Diameter of HP cylinder, $($c$)$ Power required to drive HP cylinder.