QUESTION $4(20)$

A cold room with the external dimension of $4\mathrm{.}0$ m x $2\mathrm{.}0$ m x $2\mathrm{.}0$ m is made of the insulation material of polystyrene with thickness of $150$ mm$,$ whose thermal conductivity is $0\mathrm{.}035$ W$/$m$.$K$,$ and two metal sheet layers covering on the internal and external surfaces of the insulation material, the metal sheet thickness is $2$ mm and its thermal conductivity is $50\mathrm{.}0$ W$/$m$.$K$,$ the convective heat transfer coefficient on external and internal surfaces are $5$ and $20$ w$/$m$*.$K$,$ respectively. The cold room with the indoor temperature of $-20\mathrm{.}0\backslash$deg C is used in Pretoria to process $500$kg fresh garlics from $25\backslash$deg C to $-15\backslash$deg C in $3$ hours, the average respiration heat of garlic in the processing temperature range is $10$ mW$/$kg$.$ The $3-$phase motor used to drive the evaporator fans is rated at $1\mathrm{.}5$KW$,$ both the motor and the driving equipment are located inside of the cold room, the heat loads from lighting and air infiltration are ignored, and $10\%$ of safety factor is considered. The refrigeration system has a COP of $3.$ Calculate:

$(1)$ the heat load on the evaporator

$(2)$ the heat load on the condenser

$(3)$ the electrical power required for the compressor if the overall compressor efficiency is

$80\%.$