In winters ice forms on the surface of a lake. Due to abnormal expansion of water the temperatur...

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In winters ice forms on the surface of a lake. Due to abnormal expansion of water the temperature of the water at the bottom of the lake remains constant at \( 4^{\circ} \mathrm{C} \) and we assume that
\( \mathrm{P} \) the amount of heat required to maintain this temperature of the bottom layer of water may come from the bed of the lake. If W surrounding temperature is \( -10^{\circ} \mathrm{C} \), Prove that ice formed from the surface of the lake attains a maximum thickness. Find the maximum depth from surface upto which ice is formed if the depth of lake is \( 1 \mathrm{~m} \). Given that thermal conductivity of ice is \( 0.5 \) \( \mathrm{W} / \mathrm{m}^{\circ} \mathrm{C} \).
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