Air enters a compressor operating at steady$-$state at $22$oC$,100$ kPa, and with a

volumetric flow rate of $9$ m$3/$min and exits from the compressor at $157$oC and $500$ kPa. Cooling

water is circulated through a water jacket enclosing the compressor at a rate of $10$ kg$/$min$,$

entering at $15$oC and exiting at $23$oC with a negligible change in pressure. a$)$ the power input into the compressor, and

b$)$ the rate of entropy production for this process