A room is maintained at $25$C using a vapor$-$compression refrigeration cycle with R$-134$a as the refrigerant. Heat is rejected to the condenser by cooling water entering at $20$C and exiting at $28$C$,$ with a flow rate of $0\mathrm{.}13$ kg$/$s$.$ The refrigerant enters the condenser at $1\mathrm{.}2$ MPa and $50$C and exits as a saturated liquid. If the compressor consumes $1\mathrm{.}9$ kW of power, determine:

$($a$)$ The refrigeration load in kWh and the coefficient of performance $($COP$).$

$($b$)$ The exergy efficiency of the refrigerator and the total exergy destruction in the cycle.

$($c$)$ The exergy efficiency and exergy destruction for each component of the cycle.

Take T$0=20$CT$\_0=20^\backslash$circ$\backslash$text$\{$C$\}$T$0=20$C and cp$,$water$=4\mathrm{.}18$kJ$/$kg