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When the air temperature is below 0 C, the water at the surface of a lake...

When the air temperature is below 0 C, the water at the surface of a lake freezes to form an ice sheet. The longer the air remains at this temperature, the thicker the ice sheet will become. Will a lake in Minnesota that is uniformly 40 m deep ever freeze solid? To answer this, calculate how long it would take to freeze all the water in the lake. Assume that the upper surface of the ice sheet is steady at -10 C and the bottom surface is at 0 C, and that all heat transfer occurs via conduction through the ice. (Hint: this is not a steady-state problem, and requires an integral.)

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