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 is

Options

A. `1.1 m`
B. `0.4 m`
C. `2.1 m`
D. `3.6 m`

Answer

A

Explanation

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`,