A hermetically sealed electric motor compressor combination with isentropic efficiency of $60\%,$ receives R$134$a vapour from an evaporator where the saturation temperature is $-2C.$ The vapour leaves the evaporator with $2C$ of superheat and travels to the compressor in a well$-$insulated suction pipe. The cooling capacity achieved in the evaporator is $9\mathrm{.}0+0.xkW$ where X is the last digit of one student number, e$.$g$.$ student number is $3334568,$ so $Q^{}=8\mathrm{.}8kW.$ The condenser saturation temperature is $44C.$ Refrigerant $($R$134$a$)$ leaves the condenser as a liquid sub cooled by $4C,$ and travels directly to the throttle without change in temperature:

a$)(10$ marks$)$ Sketch the cycle on a pressure$-$enthalpy diagram with $60\%$ isentropic efficiency compression. From your sketch provide the enthalpy values $($read values from your plot$)$ at each stage of the cycle. Using these values, determine the enthalpy change in the condenser, and evaporator?

b$)$ As a comparative study, use the thermophysical properties table for R$134$a$,$ calculate the net enthalpy change for an isentropic compression $($in the compressor stage$).$ Show the steps on how you obtain the enthalpy values.