A tank of water has been outdoors in cold weather, and a slab of ice 5 cm thick has formed on its surface. The air above the ice is -10C. Calculate the rate of ice formation ( in cm / h) on the ice slab. Take the thermal conductivity of ice to be 0.004 cal / (s.cm.C) and its density to be 0.92 g/cm^3. Assume no energy transfer through the tank walls or bottom.
P(conducted) = Q/t = kA (T2-T1)/ Length
p(density) = m/v
Q = Lm heat of transformation
The Attempt at a Solution
When they say on the slab, they must mean underneath it right?
Also they provide standard info the in the question like the conductivity of ice which I could look up in a table. I could similarly look up density and conductivity of water but since they didnt explicidly mention that too, I wonder if I'm not supposed to? Like maybe thats variable in terms of the problem?
Since they arent just asking the rate of conductivity through ice I probably need to use the heat of fusion formulae somewhere too.
So I need to relate the density somehow, in order to cancel out the Area which I dont have.
Pluggin in info for the conduction rate equation I get
P = 0.004A (0--10) / 5
P = A x 0.008
now for density
p = m/v = m/Ah (using A and h cuz I have more information about that, than just V)
0.92 = mA5
I don't see an obvious relation.
(heat of fusion from water to ice = 333)
Q = Lm
Q = 333m
Q = 333 x 0.92/5A
Uhm I don't know where im going with this. I could say both equations are equal to A, but then I still have P and m as variables