One half of a kilogram of liquid water at 273 K (0 °C) is placed outside on a day when the temperature is 261 K (-12 °C). Assume that the heat is lost from the water only by means of radiation and that the emissivity of the radiating surface is 0.60. 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).

Concepts: (i) In case (a) is the heat that must be removed to freeze the water less than, greater than, or the same as in case (b)? 

(ii) The loss of heat by radiation depends on the temperature of the radiating object.

Does the temperature of the water change as it freezes? 

(iii) The water both loses and gains heat by radiation. How, then, can heat transfer by radiation lead to freezing of the water? 

(iv) Will it take longer for the water to freeze in case (a) when the area is smaller or in case (b) when the area is larger? Calculations: For each case, (a) and (b), determine the time it takes the water to freeze into ice at 0 °C.