A Carnot refrigeration cycle operates between $12C$ and $-20C.$ The Refrigerant in the system is R$134$a and it flows through the cycle at $1\mathrm{.}00k\frac{g}{s}.$ The refrigerant is saturated liquid at the end of the heat rejection process and a saturated vapor at the at the end of the compression process. The net work input to the cycle is $39\mathrm{.}37$ kW $.$ Answer the following questions:

a$)$ Draw the temperature$/$entropy diagram for this process

b$)$ Determine the mass fraction of refrigerant that evaporates every second during the heat addition process.

c$)$ Determine the coefficient of performance for the cycle

d$)$ Determine the heat input for the evaporation process