Will the ice crack?

Classical Mechanics Level 4

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

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

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

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


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