Question $3(20$ points$)$

A heating system must maintain the interior of a building at $T_H=23C$ when the outside temperature is $T_C=2\mathrm{.}3C.$ If the rate of heat transfer from the building through its walls and roof is $16\mathrm{.}4$ kW $,$ determine the electrical power required, in kW $,$ to heat the building using

$($a$)$ electrical$-$resistance heating,

$($b$)$ a heat pump whose coefficient of performance is $3\mathrm{.}3,$

$($c$)$ a reversible heat pump operating between hot and cold reservoirs at $23C$ and $2\mathrm{.}3C,$ respectively.