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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 the amount of heat required to maintain this temperature of the bottom layer of water may come from the bed of the lake. If 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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