$4.)$ An ideal double evaporator refrigerating system with a high pressure and lowpressure evaporator uses R$134$a as a refrigerant. $8$ kW of cooling load in the lowpressure evaporator is achieved. The high$-$pressure evaporator operates at $0C,$ while the low$-$pressure evaporator operates at $-25C.$ The vapour leaving both the highpressure and low$-$pressure evaporator saturated. The high$-$pressure evaporator throttles the vapour to the mixing chamber, while the low$-$pressure evaporator feeds the saturated vapour directly to the mixing chamber. The mass flow rate through the compressor is $0\mathrm{.}1k\frac{g}{s}.$ The condenser pressure is $8\mathrm{.}8351$ bar, and the condenser throttles the saturated liquid refrigerant directly to the high$-$ and low$-$pressure evaporator. For the given system, calculate:

a$)$ the mass flow rate in the high pressure evaporator

b$)$ the state of the refrigerant vapour at entry to the compressor

c$)$ the cooling load achieved by the high pressure evaporator

d$)$ the work done by the compressor in kW

e$)$ the COP