Problem $1$:

A commercial refrigerator with R$-290$ 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 a rate of $0\mathrm{.}25k\frac{g}{s}$ and leaves at $26C.$ The refrigerant enters the condenser at $1\mathrm{.}2$ MPa and $100C$ and leaves at $30C.$ 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. Using EES, determine

$($a$)$ the quality of the refrigerant at the evaporator inlet,

$($b$)$ isentropic efficiency of the compressor,

$($c$)$ the refrigeration load,

$($d$)$ the COP of the refrigerator,

$($e$)$ the Carnot COP of the refrigerator,

$($f$)$ the theoretical maximum refrigeration load for the same power input to the compressor, and

$($g$)$ sketch the P$-$h and T$-$s diagrams of the cycle.