Consider the situation of the previous problem. Assume that the temperature of the water at the botton of the lake remains constant at `4^(@)C` as the ice forms on the surface (the heat required to maintain the temperature of the bottom layer may come from the bed of the lake). The depth of the lake is `1.0m`. Show that the thickness of the ice formed attains a steady state maximum value. Find this value. The thermal conductivity of water `=0.50Wm ^(-1).^(@)C^(-1)` . Take other relevent data form the previous problelm.

Explanation

When heat current in water and ice is same, steady state is reached
`i= (4 - 0)/(R_(w)) = (0 - (-10))/(R_(ice))`
`4 R_(ice) = 10 R_(w)`
`4 (x)/(K_(ice) A) = 10 ((1 - x))/(K_(w) A)`
`(4 x)/(1.7) = (10 - 10x)/(0.5)`
`2x = 17 - 17 x`
`x = (17)/(19) m = 0.89 m`