The gradient of the melting line of water on a p–T diagram close to 0∘C is −1.4×107 Pa K−1. At 0∘C, the specific volume of water is 1.00×10−3 m3 kg−1 and of ice is 1.09×10−3 m3 kg−1. Using this information, deduce the latent heat of fusion of ice.
In winter, a lake of water is covered initially by a uniform layer of ice of thickness 1 cm. The air temperature at the surface of the ice is −0.5∘C. Estimate the rate at which the layer of ice begins to thicken, assuming that the temperature of the water just below the ice is 0∘C. You can also assume steady-state conditions and ignore convection.
The temperature of the water at the bottom of the lake, depth 1 m, is maintained at 2∘C. Find the thickness of ice that will eventually be formed.
[The thermal conductivity of ice is 2.3 W m−1 K−1 and of water is 0.56 W m−1 K−1.]