HW#$7-8(15pt$ A commercial refrigerator with R$-134$a as the working fluid is used to keep the refrigerated space at $-30C$ by rejecting its waste heat to cooling water that enters the condenser at $18C$ at $0\mathrm{.}25k\frac{g}{s}$ and leaves at $26C.$ The refrigerant enters the condenser at $1\mathrm{.}2$ MPa and $65C$ and leaves at $42C.$ The inlet state of the compressor is $60$kPa and $-34C$ and the compressor is estimated to gain a net heat of $450$ W from the surroundings. Determine $(a)$ the quality of the refrigerant at the evaporator inlet, $($b$)$ the refrigeration load, $($c$)$ the COP of the refrigerator, and $($d$)$ the theoretical maximum $($totally reversible$)$ refrigeration load for the same net power input to the system.