A vapour compression refrigeration system works between the pressure limits of $0\mathrm{.}74$ bar and $8\mathrm{.}72$ bar. The refrigerant used in the system is R$134$a$.$ Refrigerant temperatures at the outlet of evaporator is $30C,$ at the exit of the compressor $88C,$ exit of condenser $33C$ and at exit of expansion valve is $9\mathrm{.}1C.$ Condenser water inlet temperature is $29\mathrm{.}5C$ and outlet temperature is $35\mathrm{.}4C.$ The water flow rate to the condenser is $24c\frac{m^3}{s}.$ The power required to drive the compressor is $360$ W $.$ Calculate the following, $($i$)$ Mass flow of refrigerant, $($ii$)$ Refrigerating capacity, $($iii$)$ Heat rejected by the condenser, $($iv$)$ Actual COP of the system. $($solve using p$-$h chart$)$