# A 0.307-m-thick sheet of ice covers a lake. The air temperature at the ice surface is -15.1 °C. In 5.40 minutes, the ice thickens by a small amount. Assume that no heat flows from the ground below into the water and that the added ice is very thin compared to 0.307 m. Calculate the number of millimeters by which the ice thickens. Do not enter unit.

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A 0.307-m-thick sheet of ice covers a lake. The air temperature at the ice surface is -15.1 °C. In 5.40 minutes, the ice thickens by a small amount. Assume that no heat flows from the ground below into the water and that the added ice is very thin compared to 0.307 m. Calculate the number of millimeters by which the ice thickens. Do not enter unit.

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Step 1

The liquid water directly beneath the ice sheet is in equilibrium with the solid ice and has temperature equal to  . The water is hotter than the air above the ice sheet so that the water will loss heat due to thermal conduction through the ice. The equation for the rate of heat flow through ice using the Fourier’s law is given by

Step 2

The loss of heat causes some water to freeze. The amount of heat lost in terms of the amount of ice formed can be written as

Step 3

Equate equations (1) and (4) ...

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### Heat Transfer 