Ice has formed on a shallow pond, and a steady state has been reached, with the air above the ice at $-5.0^0\mathrm{C}$ and the bottom of the pond at ${\text{4.0}}^0\mathrm{C}$. 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 ${\mathrm{C}}^0\mathrm{s},$ respectively.) The thickness of ice layer is

The top surface of the ice is at ${\mathrm{T}}_{\mathrm{C}}= -5.0^0\mathrm{C}$ and the bottom of the body of water is at ${\mathrm{T}}_{\mathrm{H}} = 4.0^0\mathrm{C} \mathrm{and}$$\mathrm{the} \mathrm{interface} \mathrm{between}$ 

$\mathrm{the} \mathrm{ice} \mathrm{and} \mathrm{the} \mathrm{water} \mathrm{is} \mathrm{at} {\mathrm{T}}_{\mathrm{x}}= 0.0^0\mathrm{C}$. The rate of heat flow through both layers should be equal

      $\frac{{\mathrm{k}}_{\mathrm{water}}\mathrm{A}({\mathrm{T}}_{\mathrm{H}}-{\mathrm{T}}_{\mathrm{X}})}{\mathrm{L}-{\mathrm{L}}_{\mathrm{ice}}} = \frac{{\mathrm{k}}_{\mathrm{ice}}\mathrm{A}({\mathrm{T}}_{\mathrm{X}}-{\mathrm{T}}_{\mathrm{C}})}{{\mathrm{L}}_{\mathrm{ice}}}$

We cancel the area A and solve for thickness of the ice layer: ${\mathrm{L}}_{\mathrm{ice}} = 1.1 \mathrm{m}.$