# Freezing Lake - Heat Energy Questions

## Homework Statement

Freezing Lake
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?

## Homework Equations

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?

Thank you.

Simon Bridge
Homework Helper
For (a) ... the water just below the ice is still a liquid ... what is the coldest water can get without freezing?

I figured that out... I am working on part c) and d) now. The coldest the water can get is 0°C without completely freezing.

Thank you for your assistance. :)

Simon Bridge
Homework Helper
No worries: it is common that even just writing down the question leads to the answer.

Helps to show your working for a and b though ... part of the point of these forums is so that your difficulties can help others in the same fix later: you may have the answers now but others googling to your question may be yet to find them.

Tell me when you are next stuck.

I am actually stuck on this question too. I managed to figure part A out on my own but I'm stuck on part B.

CWatters
Homework Helper
Gold Member
Think about what the heat loss is likely to be proportionate to.

For example the heat loss from a building is likely to be proportional to the temperature difference between the inside and outside, the type of insulation etc and inversely proportional to the thickness of the insulation. What's the simplest way you can write that out.

Simon Bridge