# A very hard question about specific heat.

1. Feb 20, 2007

### dingdong_mustaf

A pond of water at 0°C is covered with a layer of ice 4.50 cm thick. If the air temperature stays constant at -11.0°C, how much time does it take for the thickness of the ice to increase to 9.00 cm?

Hint: To solve this problem, use the heat conduction equation,

dQ/dt = kA delta T/x

and note that the incremental energy dQ extracted from the water through the thickness x is the amount required to freeze a thickness dx of ice. That is, dQ = LpA dx, where p is the density of the ice, A is the area, and L is the latent heat of fusion. (The specific gravity and thermal conductivity for ice are, respectively, 0.917 is 2.0 W/m/°C.)

I dont have much of an idea on how to attempt this question, all ive got so far is.

dQ = LpA dx
so LpA dx/dt = kA delta T/x
x/dt = L delta T/ L p dx

I guess thats useful as it gets rid of surface area in the equation ( which isnt given), but im not sure where to go from there. Also, delta T would be zero, and so the entire equation would equal zero, which doesnt make much sense to me.

By the way im 16 and so presume that im very ignorant.

2. Feb 20, 2007

### f(x)

why should dT be 0? Outside temp is -11 while water is at 0.

dQ=KA.(T1-T2)/x .dt where T1-T2=11
dQ=mL=dx.A.P.L
so we have from above eqns.
dx.A.P.L=KA.11/x .dt
xdx.P.L=K.11 dt
integrate LHS from 0.045 to 0.09 and RHS from 0 to t, where t is the required time.
P.L.(x^2)/2=22t
substituing the values (L=3.36 x 10^5)& solving i get t=42.5 sec

IMO this is too small a value, anyway, do tell the answer :)