1.

Ice has formed on a shallow pond, and a steady state has been reached, with the air above the ice at `-5.0^(@)C` and the bottom of the pond at `40^(@)C`. If the total depth of ice + water is `1.4 m`, (Assume that the thermal conductivities of ice and water are `0.40` and `0.12 cal//m C^(@)s`, respectively.) The thickness of ice layer isA. `1.1 m`B. `0.4 m`C. `2.1 m`D. `3.6 m`

Answer» Correct Answer - A
The top surface of the ice is at `t_(C) =-5.0^(@)C` and teh bottom of the body of water is at `T_(H) = 4.0^(@)C` and the interface between the ice and the water is at `T_(X) = 0.0^(@)C`. The rate of heat flow through both layers should be equal
`(k_("water")A(T_(H)-T_(X)))/(L-L_("ice")) = (k_(ice)A(T_(X)-T_(C)))/(L_("ice"))`
We cancel the area `A` and solve for thickness of the ice layer:`L_("ice") = 1.1 m`,


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