When the air temperature is below 0.0°C, the water at the surface of a lake freezes to form an ice sheet. As the temperature approaches 0.0°C, the coldest water rises to the top and begins to freeze while the slightly warmer water, which is more dense, will be beneath the surface. Thickness of the ice sheet formed on the surface of a lake is proportional to the square root of the time if the heat of fusion of the water freezing on the underside of the ice sheet is conducted through the sheet and can be expressed by the formula: 2k(Tr-Tc) vt h= pl a) Assuming that the upper surface of the ice sheet is at -10∘C and the bottom surface is at 0∘C, calculate the time it will take to form an ice sheet 30 cm thick.
Express your answer in seconds.
b) If the lake in part is uniformly 50 m deep, how long would it take to freeze all the water in the lake?
Express your answer in seconds.