$2)(35$ points$)$ A vapor$-$compression refrigerator uses two stages of compression and flash intercooling as a means of reducing total compression work. On the next two pages, a description of the process, taken from section $10\mathrm{.}4\mathrm{.}3$ in Moran and Shapiro, is attached. The refrigerator has a cooling capacity of $70$ kW $.$ The condenser pressure is $1$ MPa $,$ while the direct contact heat exchanger and flash chamber are at $0\mathrm{.}5$ MPa $.$ Saturated liquid at $1$ MPa exits the condenser while saturated vapor at $\backslash (-20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ exits the evaporator. Saturated liquid at $0\mathrm{.}5$ MPa enters the expansion valve below the flash chamber. The refrigerant is R$-22$; assume that both compressors are isentropic$.$

A$)$ What is the quality of the two$-$phase mixture separated in the flash chamber.

B$)$ What is the mass flow rate $(\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$s$\}\backslash ))$ of R$-22$ through the evaporator?

C$)$ What is the mass flow rate $(\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$s$\}\backslash ))$ of R$-22$ through the condenser?

D$)$ What is the power $($ kW $)$ required to run the first compressor stage $($immediately downstream of the evaporator$)?$ Note that two$-$parameter interpolation is required to find the outlet state of the first compressor stage.

E$)$ What is the power $($kW$)$ required to run the second compressor stage? Hint: To find the inlet state state $3$ in Fig. $10\mathrm{.}10-$ an energy balance must be carried out on the direct contact heat exchanger.

F$)$ What is the refrigerator's coefficient of performance?