Question $1$

A two$-$stage piston air compressor deals with $14m^3$ of free air per minute; free air conditions

being $98$ kPa and $18C.$ The delivery pressure is $3\mathrm{.}1$ MPa $,$ the law of compression being $P{V}^{1\mathrm{.}25}$

$=$ constant throughout. Conditiond in the compression cylinder during the suction stroke are

$90$ kPa and $27C.$ Intercooling is complete and the mechanical efficiency is $75\%.$ Calculate:

a The intermediate pressure for minimum work

b The corresponding power of the driving motor

c The heat transfer per second in the intercooler

For air take $R=287\frac{J}{k}g*K$ and $C_p=1\mathrm{.}005k\frac{J}{k}g*K$