A small pond has a layer of ice 1cm thick floating on its surface. The air temperature is -10°C. Steps (a-c) should help you find the final answers in (d) and (e).
(a) What is the temperature of the liquid water just below the ice?
(b) Write the expression for the rate of heat transfer through the ice as a function of thickness of the ice?
(c) Write the expression for the rate of heat flow required to freeze the water? Hint: first find how much heat must be removed to freeze a given thickness of ice.
(d) Find the rate in cm/hr at which ice is added to the layer.
(e) How long does it take for a 20cm layer to build up?
Q = mcΔT (temperature change)
Q = mL (phase change)
The Attempt at a Solution
I cannot begin the other parts of this question without having the first part answered and I am stuck right in the beginning. I need a booster to help me get started and to push along this question. At the moment, I attempted to solve part (a) and figured that there are no calculations involved; I assume that the water just below the ice would be at 0°C since that immediate area between ice and water in contact is where the phase change occurs. However, I might be wrong. Anyone here willing to guide me in the right direction?