A heat pump has a coefficient of performance equal to $4\mathrm{.}50$ and requires a power of $1\mathrm{.}63$ kW to operate.

$($a$)$ How much energy does the heat pump add to a home in one hour?

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$($b$)$ If the heat pump is reversed so that it acts as an air conditioner in the summer, what would be its coefficient of performance?

$($b$)$ Determine the coefficient of performance of the refrigerator.