A two$-$stage vapour compression refrigeration system $($Fig$.1)$ with R$134$a as the refrigerant, uses flash chamber to remove flash gas. The pressure of the condenser and the flash tank are $1\mathrm{.}2$MPa,$0\mathrm{.}6$MPa respectively. The evaporator temperature is $-20C.$ The states of the refrigerant at the exit of the condenser and the evaporator are saturated. The capacity of the system is $5$ TR$.$ Determine $($i$)$ refrigeration capacity of the system, $($ii$)$ work input to the compressors and the $($iii$)$ COP of the system. Show the process on the p$-$h diagram.

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