Question $2(20$ points$)$

By removing energy by heat transfer from a room, a window air conditioner maintains the room at $28C$ on a day when the outside temperature is $38C.$

$($a$)$ Determine, in kW per kW of cooling, the minimum theoretical power required by the air conditioner.

$($b$)$ To achieve required rates of heat transfer with practical$-$sized units, air conditioners typically receive energy by heat transfer at a temperature below that of the room being cooled and discharge energy by heat transfer at a temperature above that of the surroundings. Consider the effect of this by determining the minimum theoretical power, in kW per kW of cooling, required when $T_C=18C$ and $T_H=38C,$ and compare with the value found in part $($a$).$