Will the ice crack?

Ice has formed on a shallow pond and a steady state has been reached, with the air (above the ice) at 5oC\displaystyle -5^o C, and the bottom of the pond at 4oC\displaystyle 4^o C.

If the total depth of ice + water\displaystyle \text{ice + water} is 1.4m\displaystyle 1.4m, then find the thickness of the ice (in m) layer on the pond.

Details and Assumptions:
\bullet Kice=0.4cal/moC\displaystyle K_{ice} = 0.4 \text{cal}/m-^oC
\bullet Kwater=0.125cal/moC\displaystyle K_{water} = 0.125 \text{cal}/m-^oC, where K\displaystyle K denotes the thermal conductivity.

Note: This problem appeared in our AITS (All India Test Series)


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