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243.


Problem 25.59 (RHK)


Ice has formed on a shallow pond and a steady state has been reached with the air above the ice at and the bottom of the pond at . The total depth of ice water is 1.42 m. We have to find how thick the ice is. We may assume that the thermal conductivities of ice and water are 1.67 and


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 Let the thickness of ice be h m. The total depth of ice water is 1.42 m. Therefore, the water depth below the ice surface to the bottom of the tank will be .

Temperature of water in contact with the ice slab will be . Temperature of air above the ice surface is . Therefore the temperature difference across the ice-surface is

Temperature at the bottom of the pond is . Therefore, the temperature difference between that of the bottom of the pond and the bottom layer of the ice surface will be

Thermal conductivity of water is

The thermal conductivity of ice is

In the condition of steady state the rate of loss of heat from the bottom of the pond per will be equal to the rate of heat flow per through the ice to the air above the ice surface. That is

or

or

or