In a 20m deep lake, the bottom is at a constant temperature of 4°C. The air temperature is constant at -10°C. The thermal conductivity of ice is 4 times that water. Neglecting the expansion of water on freezing, the maximum thickness of ice will be
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Question

In a 20m deep lake, the bottom is at a constant temperature of 4°C. The air temperature is constant at -10°C. The thermal conductivity of ice is 4 times that water. Neglecting the expansion of water on freezing, the maximum thickness of ice will be

Options

G1 Physics · Accepted Answer

At steady state the heat current through the ice layer equals that through the remaining water layer. If the ice thickness is x, then kᵢ(10)/x = kw(4)/(20−x). Given kᵢ=4kw, 40/x = 4/(20−x). Hence 800−40x=4x, so x=200/11 m. Option B.

In a 20m deep lake, the bottom is at a constant temperature of 4°C. The air temperature is constant at −10°C. The thermal conductivity of ice is 4 times that water. Neglecting the expansion of water on freezing, the maximum thickness of ice will be