A two$-$stage single$-$acting compressor is required to deliver air at $7$ MPa from an induction

pressure of $100$ kPa $,$ at a rate of $2\mathrm{.}4\frac{m^3}{m}in$ measured at free air conditions of $101\mathrm{.}3$ kPa and

$15C.$ The intermdeiate pressure is ideal and intercooling is perfect. The index of compression

for both stages is $1\mathrm{.}25,$ and the temperature at the end of induction stroke in each cylinder is

$32C.$ The speed of the compressor is $750$ rpm $.$

a Determine the polytropic power

b Determine the swept volumes of the cylinders

c If the mechanical efficiency of the compressor is $85\%,$ determine the power

output of the motor.