Question $4(25$ points$)$

The refrigerator shown in the figure below steadily receives a power input of $0\mathrm{.}18$ kW while

rejecting energy by heat transfer to the surroundings at a rate of $0\mathrm{.}68$ kW $.$ Determine

$($a$)$ the rate at which heat is removed from the refrigerated space, in kW $,$

$($b$)$ the refrigerator's coefficient of performance.