Serway & Jewett — The First Law of Thermodynamics: Problem 47.

A pond of water at \(0^\circ\text{C}\) is covered with a layer of ice \(4.00\text{ cm}\) thick. If the air temperature stays constant at \(-10.0^\circ\text{C}\), what time interval is required for the ice thickness to increase to \(8.00\text{ cm}\)? Suggestion: Use Equation 19.18 in the form \(\frac{dQ}{dt} = kA \frac{\Delta T}{x}\) and note that the incremental energy \(dQ\) extracted from the water through the thickness \(x\) of ice is the amount required to freeze a thickness \(dx\) of ice. That is, \(dQ = L_f \rho A dx\), where \(\rho\) is the density of the ice, \(A\) is the area, and \(L_f\) is the latent heat of fusion.