b$)$ Air enters an air compressor with a volumetric flow rate of $35\frac{m^3}{m}in$ at $100$kPa,$300K$ and exits with a pressure of $650$kPa and a temperature of $400K.$ The power input to the compressor is $150kW.$ The compressor is cooled by cooling water during the process. Assume air as an ideal gas with $R=0\mathrm{.}287k\frac{J}{k}g.K$ and $c_p=1\mathrm{.}005k\frac{J}{k}g.K.$ Neglect changes in kinetic and potential energies.

i$)$ Sketch the schematic diagram and label all the properties given.

ii$)$ Determine the mass flow rate of air, $k\frac{g}{s}.$

iii$)$ Calculate the heat loss, $kW.$