$(35$ pts$.)$ A vapor$-$compression refrigerator utilizes refrigerant$-134$a $($R$-134$a$)$ as the working fluid. The refrigerant flows at steady state through an evaporator, a compressor, a condenser, and an expansion $($throttle$)$ valve $($see figure$).$ The outlet of the evaporator is Saturated $R-134$a vapor at $T_1=-10C.$ The inlet to the condenser is R$-134$a at $p_2=1000$kPa and $T_2=50C.$ The outlet of the condenser is saturated $R-134$a liquid at $p_3=1000$ kPa $.$ The compressor operates adiabatically. Use the R$-134$a tables for R$-134$a data. Ignore kinetic and potential energy effects. Calculate:

$($a$)$ The amount of heat removed from the refrigerated

refrigerated space

space, $q_L,$ per kg of R$-134$a$.$

$($b$)$ The work input to the compressor, $w,$ per kg of $R-134a.$

$($c$)$ The amount of heat rejected to the surroundings, $q_H,$ per kg of R$-134$a$.$

$($d$)$ The coefficient of performance of the refrigerator.