It is time to answer the age old question: What the dog doin'? Freon Bud has built a refrigerator shown in the diagram below. The refrigerator uses R$-22$ as the working fluid. The inlet to the compressor is at $1$ bar and $-10C.$ The refrigerant is pumped up to a pressure of $12$ bar and exits the adiabatic compressor. The compressor operates at a work rate per unit mass flowing of $-24\mathrm{.}32k\frac{J}{k}g.$ The refrigerant passes through the condenser isobarically, where it is cooled to a temperature of $28C.$ Assuming kinetic and potential effects are negligible, determine the following:

a$)$ The exit temperature of the compressor in $C.T$

b$)$ The rate of energy removed via heat transfer per unit mass flowing from the refrigerant by the condenser in $k\frac{J}{k}g.$

c$)$ The coefficient of performance of cooling for the refrigeration cycle.