$3.$ 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, the flash tank and the evaporator are $1\mathrm{.}2$ MPa $,0\mathrm{.}6$ MPa, and $0\mathrm{.}1$ MPa respectively. The states of the refrigerant at the exit of the condenser and the evaporator are saturated. 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.