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On a winter day with a temperature -10C, it is observed that the lake has a 1cm thick layer of ice over the entire surface. Assuming the temperature stays constant, find how long it will take for the ice to be safe: (a) If the air temperature remains at -10C, find the rate in cm per hour at which ice is added to the layer. The thermal conductivity of ice is 2.18W/m · K. (b) Find the time that the ice layer reaches a thickness of 20 cm.

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