$6.$ The two$-$evaporator compression refrigeration system shown below uses refrigerant $\backslash (\backslash$mathrm$\{$R$\}-134\backslash$mathrm$\{$a$\}\backslash )$ as its working fluid. Evaporator $1$ operates at $\backslash (0^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ evaporator $2$ operates at $\backslash (-26\mathrm{.}37\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ and the condenser operates at $800$ kPa $.$ The compressor is isentropic$.$ The refrigerant is circulated through the compressor at a rate of $\backslash (0\mathrm{.}10\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ),$ and the lowtemperature 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$($a$).$ the cooling load $\backslash ((\backslash$mathrm$\{$kW$\})\backslash )$ at which heat is withdrawn from the "refrigerator" compartment by the high$-$temperature evaporator $($i$.$e$.,$ evaporator $1)$;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.