Question

Ice has formed on a shallow pond, and a steady state has been reached, with the air above the ice at $-5.0^{\circ }C$ and the bottom of the pond at $4.0^{\circ }C$. If the total depth of ice $+$ water is $1.4m$, (Assume that the thermal conductivities of ice and water are $0.40$ and $0.12cal/m{C}^{\circ }s$, respectively.) The thickness of ice layer is

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

Answer 1

Answer: (A)

The top surface of the ice is at $T_C=-5.0^{\circ }C$ and the bottom of the body of water is at $T_H=4.0^{\circ }C$ and the interface between the ice and the water is at $T_X$ $=0.0^{\circ }C$.
The rate of heat flow through both layers should be equal
$\frac{k_{\text{water }}A\left(T_H-T_X\right)}{L-L_{\text{ice }}}=\frac{k_{\text{ice }}A\left(T_X-T_C\right)}{L_{\text{ice }}}$
We cancel the area $A$ and solve for thickness of the ice layer: $L_{\text{ice }}=1.1m$.