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In a 10 m deep lake, the bottom is at a constant temperature of $4^{o} C .$ The air temperature is constant at $- 4^{o} C .$ The thermal conductivity of ice is 3 times that of water. Neglecting the expansion of water on freezing, the maximum thickness of ice will be

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7.5 m

6 m

5 m

2.5 m

answer is A.

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Detailed Solution

The rate of heat flow is the same through water and ice in the steady state.

$I = k A \frac{4 - 0}{10 - x} = 3 k A \frac{0 - (- 4)}{x}$

$x = (10 - x) \times 3 = 7.5 m$

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