Plow$=90$

Pintm$=320$

Phigh$=1400$ Two$-$stage, vapor$-$compression refrigeration system with two evaporators and a direct contact heat exchanger as shown in the figure. Saturated vapor R$134$a from evaporator $1$ enters compressor $1$ at the lowest Pressure $\backslash (\backslash$left$\backslash \{$P$\_\{\backslash$text $\{$low $\}\}\backslash$right$\backslash \}\backslash$mathrm$\{$kPa$\}\backslash )$ and exits at an intermediate pressure kPa $.$ Evaporator $2$ operates at $\backslash (\backslash$left$\backslash \{$P$\_\{\backslash$text $\{$intm $\}\}\backslash$right$\backslash \}\backslash$mathrm$\{$kPa$\}\backslash ),$ with saturated vapor exiting at state $8.$ The condenser pressure is the highest pressure $\backslash (\backslash$left$\backslash \{$P$\_\{$h i g h$\}\backslash$right$\backslash \}\backslash$mathrm$\{$kPa$\}\backslash ),$ and saturated liquid refrigerant exits the condenser. Each compressor stage has an isentropic efficiency of $\backslash (80\backslash \%\backslash ).$ The refrigeration capacity of evaporator $1$ is $18$ kW and for evaporator $2$ is $36$ kW $.$

A$)$ Sketch the T$-$s diagram of the cycle $($Show saturation lines, constant pressure lines, add each state properly i$.$e$.$ add values of T and s for each state$).$

B$)$ Determine each compressor's work

C$)$ Determine COP of the cycle