A single$-$acting, single$-$cylinder air compressor has a cylinder diameter of $160$ mm and a stroke of $230$ mm $.$

The clearance volume $=6\%$ of the swept volume.

Air is drawn into the cylinder at $102$ kPa and $16C.$ It is then compressed to $714$ kPa $.$

The index for compression and expansion $n=1,32.$

R for air $=0,287k\frac{J}{k}g.K.$

a$)$ Calculate the volumetric efficiency.

b$)$ Calculate the mass of air compressed per cycle.

c$)$ Calculate the power required to drive the compressor when rotating at a speed of $260\frac{r}{m}in.$