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 $1.4\, m$, (Assume that the thermal conductivities of ice and water are $0.40$ and $0.12\, cal / m C ^{\circ} s$, 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: $L_{\text {ice }}=1.1\, m$.