# Homework Help: Expansion question

1. Dec 10, 2006

### debwaldy

1. The problem statement, all variables and given/known data
hi,i was wondering if someone could tell me if the following solution makes sense,ithink it does but not sure why?

cool air blowing across the surface of a frozen lake keeps the top surface of the ice at a temperature of -5degrees celsius.what is the rate of increase in the thickness of the ice layer when the ice is 10 mm thick?

2. Relevant equations

the density,thermal conductivity and specific latent heat of fusion of ice are 920 kg m^-3, 1.7 J m^-1 K^-1 s^-1 and 3.3*10^5 J kg^-1 respectively

3. The attempt at a solution
so i said that:

the heat transfer coefficient = thermal conductivity/thickness of material
i.e heat transfer coefficient= 1.7/0.01= 1.7*10^2 J K^-1 s^-1

then i said :
heat flux=(1.7*10^2) *5 = 8.5*10^2

then:
8.5*10^2/920 = 9.23913*10^-1

and so:
9.23913*10^-1/3.3*10^5= 2.799* 10^-6 ms^-1

i know the answer is right but i dont quite understand the thinking behind it.could anyone explain it to me?
any help would be much appreciated

2. Dec 10, 2006

### AlephZero

You seem to have done the right sums, but not in a logical order.
Your heat transfer coeff. and heat flux are OK.

Now think about what happens to 1 square meter of lake surface in 1 second.

850 J of heat flows out of the lake. That freezes 850/3.3*10^5 = 2.575*10^-3 Kg of ice.

The volume of the ice is 2.575*10^-3/920 = 2.799*10^-6 m^3.

We were considering 1 square meter of area, so 2.799*10^-6 m^3 is a block of size 1m * 1m * 2.799*10^-6 m.

The time was 1 second, so the thickness changes at 2.799*10^-6 ms-1.

3. Dec 10, 2006

### debwaldy

thanks a million,that makes sense to me now alright....wasnt really thinking bout it in a logical manner
thanks for clearing that up!