Consider the situation of the previous problem. Assume that the temperature of the water at the botton of the lake remains contant 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 mamimum value. Find this value. The thermal conductivity of water `=0.50Wm ^(-1)`^(@)C^(-1)` . Take other relevent data form the previous problelm.

Answer

C

Explanation

Let B be the maximum level up to which ice is formed. Hence the heat conducted at that point form both the level is same.
`i.e, (Q_ice)/t=(Q_water)/t`
implies (K_(ice)xxAxx10)/x=(K_(water )xxAxx10)/(1-x)`
implies(1.7xx10)/x=(5xx10^(-1)xx4)/(1-x)`
implies(17)/x=(2)/(1-x)`
`implies 17-17x=2x`
`implies19x=17`
`implies x=(17)(19)=0.894m=89 cm.`