Time Needed for a Lake to Freeze Over. (a) When the air

Chapter 17, Problem 17.105

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Time Needed for a Lake to Freeze Over.

(a) When the air temperature is below 0°C, the water at the surface of a lake freezes to form an ice sheet. Why doesn’t freezing occur throughout the entire volume of the lake?

(b) Show that the thickness of the ice sheet formed on the surface of a lake is proportional to the square root of the time if the heat of fusion of the water freezing on the underside of the ice sheet is conducted through the sheet.

(c) Assuming that the upper surface of the ice sheet is at -10°C and the bottom surface is at 0°C, calculate the time it will take to form an ice sheet 25 cm thick.

(d) If the lake in part (c) is uniformly 40 m deep, how long would it take to freeze all the water in the lake? Is this likely to occur?