A freezer that operates on a Carnot cycle maintains an interior temperature of \(-18{ }^{\circ} \mathrm{C}\) and exhausts thermal energy into a kitchen at \(22^{\circ} \mathrm{C}\). You place a tray containing \(0.500 \mathrm{~kg}\) of water at \(0^{\circ} \mathrm{C}\) in the freezer and observe that the freezer draws electrical energy at a rate of \(115 \mathrm{~W}\).

(a) How long does it take to transform all the water to ice?

(b) What is the freezer's coefficient of performance of cooling?

(c) How much thermal energy is exhausted into the kitchen during the time interval it takes to freeze the water?

(d) What is the change in entropy of the water as it freezes?

(e) What is the change in entropy of the system that consists of the water plus the kitchen? For water, the specific transformation energy for melting is \(L_{\text {melting }}=334 \mathrm{~kJ} / \mathrm{kg}\).