The two$-$evaporator compression refrigeration system shown below uses refrigerant R$-134$a as its working fluid. Evaporator $1$ operates at $0$C$,$ evaporator $2$ operates at $-26\mathrm{.}37$C$,$ and the condenser operates at $800$ kPa. The compressor is isentropic$.$ The refrigerant is circulated through the compressor at a rate of $0\mathrm{.}10$ kg$/$s$,$ and the low temperature

evaporator $($i$.$e$.,$ evaporator $2)$ services a cooling load of $8\mathrm{.}0$ kW as the rate of heat withdrawal from the $$freezer$$ compartment. The refrigerant exits the condenser as a saturated liquid, at it exits each evaporator as a saturated vapor. The expansion valves throttle the

saturated liquid refrigerant exiting the condenser to the corresponding pressure at which each evaporator operates. The pressure$-$reducing valve likewise throttles the saturated vapor exiting evaporator $1$ to a pressure identical to that of the saturated vapor exiting evaporator $2.$

Determine the following:

$($a$).$ the cooling load $($kW$)$ at which heat is withdrawn from the $$refrigerator$$ compartment by the high$-$temperature evaporator $($i$.$e$.,$ evaporator $1)$;

$($b$).$ the power $($kW$)$ required for the compressor; and

$($c$).$ the coefficient of performance $($COP$)$ of the refrigeration system.