(a) If the heat pump from the refrigerator in Example 21.7 is used during the winter to heat a room to \(20^{\circ} \mathrm{C}\) when it's \(4{ }^{\circ} \mathrm{C}\) outside, what is \(\mathrm{COP}_{\text {heating }}\) ?

(b) At what rate must work be done on the heat pump if you want to heat the room at a rate of \(500 \mathrm{~W}\) ?

Data from Example 21.7

The thermal insulation in a refrigerator is never perfect. Typically energy is transferred thermally from the room to the refrigerator interior at a rate of \(60 \mathrm{~W}\) with the refrigerator door closed. Suppose the interior needs to be held at \(4.0^{\circ} \mathrm{C}\) and the temperature of the room is \(20^{\circ} \mathrm{C}\). At what minimum rate must mechanical energy be delivered to the refrigerator to maintain the interior at \(4.0^{\circ} \mathrm{C}\) ?