One half of a kilogram of liquid water at 273 K (0°C) is placed outside on a day when the temperature is 257 K (-16°C). Assume that the heat is lost from the water only by means of radiation and that the emissivity of the radiating surface is 0.600. Consider two cases: when the surface area of the water is (a) 0.035 m² (as it might be in a cup) and (b) 1.5 m² (as it could be if the water were spilled out to form a thin sheet). For each case, (a) and (b), determine the time it takes the water to freeze into ice at 0°C.