A four$-$cylinder, single acting R$-12$ compressor $30$ cm x $40$ cm runs at $960$ rpm$.$ The compressor clearance factor is $0\mathrm{.}03$ and the law of compression pV$1\mathrm{.}1=$C$.$ the operating pressures for the vapour compression refrigeration system are: $8\mathrm{.}47$ bar $(35\backslash$deg C$)$ and $1\mathrm{.}004$ bar $(-30\backslash$deg C$).$ The refrigerant temperatures are: entering the compressor $-20\backslash$deg C$,$ leaving the compressor $50\backslash$deg C; entering the condenser $45\backslash$deg C$,$ leaving the condenser $25\backslash$deg C$,$ entering the expansion valve $30\backslash$deg C and leaving the evaporator dry saturated. Assuming that heat removed in the compressor is $25$ kJ$/$sec$.$ calculate: i$)$ The refrigerating capacity ii$)$ The compressor power iii$)$ COP iv$)$ Mass of condensing cooling water assuming the rise in temperature to be $10\backslash$deg C v$)$ Also tabulate energy balance for $1$ kg of refrigerant.