# (Rate of Heat Flow)

1. Oct 5, 2014

### Morteza Rahimi

1. The problem statement, all variables and given/known data

The same question was asked on this forum about two years ago, however I did not find any of the given answers clear. The question was the following:

A small pond has a layer of ice 1cm thick floating on its surface. The air temperature is -10C.

(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?

2. Relevant equations

H = dQ/dt = kA(TH - TC)/L

3. The attempt at a solution

for part b, I attempted to derive H with respect to L, and got the following:

dH/dL = -kA(TH - TC)/L2

I am not sure if I am misunderstanding what the question wants from me, and would appreciate any guidance anyone provides.

2. Oct 5, 2014

### Staff: Mentor

If A is the surface area and $\Delta x$ is the thickness of ice that gets frozen during the time interval $\Delta t$, what volume of ice gets frozen during the time interval $\Delta t$? What is the mass of ice that gets frozen during the time interval $\Delta t$? How much heat has to be removed from the mass during the time interval $\Delta t$ to freeze this mass of ice?

Chet