Problem $2(25$ points$)$

A commercial refrigerator with refrigerant$-134$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 a rate of $0\mathrm{.}25k\frac{g}{s}$ 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. Do the following:

a$)$ Draw this cycle on a T$-$s diagram.

b$)$ Determine the quality of the refrigerant at the evaporator inlet.

c$)$ Determine the refrigeration load.

d$)$ Determine the COP of the refrigerator.

e$)$ Determine the theoretical maximum refrigeration load for the same power input to the compressor. You may consider the cooling water to be a thermal reservoir with a constant temperature of $18C.$ Assume the reversed Carnot cycle with an adiabatic compressor.