Problem $1.(35$ pts $)$ A refrigeration cycle as shown uses Refrigerant $134$ a as the working fluid to maintain a cold space at $25F$ in a $70F$ environment. The refrigerant leaves the evaporator as saturated vapor at $20lb\frac{f}{i}{n}^2$ and enters the cool end of the heat exchanger. The heat exchanger raises the temperature of the fluid to $80F$ before it enters the compressor which increases its pressure to $200lb\frac{f}{i}{n}^2.$ The fluid leaves the condenser as saturated liquid and enters the hot end of the heat exchanger. Assuming a compressor isentropic efficiency of $88\%$ and neglecting the pressure drop across the heat exchanger, evaporator, and condenser,

a$)$ show the cycle on a T$-$s diagram then calculate:

b$)$ the coefficient of performance of the refrigeration cycle,

c$)$ the maximum coefficient of performance that can be attained with this cycle, and

d$)$ the coefficient of performance if the cycle is operated as a heat pump.