The air above the surface of a freshwater lake is at a temperature T4, while the water is at its freezing point T, where T, < T,. After a time t has elapsed, ice of thickness y has formed. Assuming that the heat, which is liberated when the water freezes, flows up through the ice by conduction and then into the air by natural convection, prove that y T-TA h 2K PL where h is the convection coefficient per unit area and is assumed constant while ice forms, K is the thermal conductivity of ice, / is the latent heat of fusion of ice, and pis the density of ice. (Hint: The temperature of the upper surface is variable. Assume that the ice has a thickness y and imagine an infinitesimal thickness dy to form in time dt.) The air above the surface of a freshwater lake is at a temperature T4, while the water is at its freezing point T, where T, < T,. After a time t has elapsed, ice of thickness y has formed. Assuming that the heat, which is liberated when the water freezes, flows up through the ice by conduction and then into the air by natural convection, prove that y T-TA h 2K PL where h is the convection coefficient per unit area and is assumed constant while ice forms, K is the thermal conductivity of ice, / is the latent heat of fusion of ice, and pis the density of ice. (Hint: The temperature of the upper surface is variable. Assume that the ice has a thickness y and imagine an infinitesimal thickness dy to form in time dt.)