$2.$ Consider a two$-$stage compression refrigeration system operating between the pressure limits of $1\mathrm{.}4$

and $0\mathrm{.}12$ MPa. The working fluid is refrigerant$-134$a$.$ The refrigerant leaves the condenser as a

saturated liquid and is throttled to a flash chamber operating at $0\mathrm{.}5$ MPa. Part of the refrigerant

evaporates during this flashing process, and this vapor is mixed with the refrigerant leaving the

low$-$pressure compressor. The mixture is then compressed to the condenser pressure by the high$-$

pressure compressor. The liquid in the flash chamber is throttled to the evaporator pressure, and it

cools the refrigerated space as it vaporizes in the evaporator. Assuming the refrigerant leaves the

evaporator as saturated vapor and both compressors are isentropic$,$ determine $($a$)$ the fraction of the

refrigerant that evaporates as it is throttled to the flash chamber, $($b$)$ the amount of heat removed

from the refrigerated space and the compressor work per unit mass of refrigerant flowing through

the condenser, and $($c$)$ the coefficient of performance.