Heat Transfer

Question

Suppose a lake has a layer of ice 12 cm thick on its surface. The top of the ice layer is cooled by the atmosphere to -5.45° C. The lower surface is in contact with water at 0.0° C. The thermal conductivity of ice is 0.004 cal/(s · cm · C°).

 

(a) At what rate is heat transferred through a 1.1 cm^2 area of the ice?

(I figured this one out.  The answer is 0.00200 cal/s.)

 

(b) How long will it take to freeze an additional 1.1 mm of ice onto the lower surface of the ice?

(Do I apply H = Q/t ?)

Answer 1

You have the rate of heat transfer, so the question is how long will it take to transfer the heat of fusion for the relevant amount of ice.   The volume of ice is just 1.1cm^2 * 1mm  (change the units to something reasonable).   Use the density of water to convert to grams and then use the heat of fusion to determine how much heat is required.

 

Yes, this is a simple rate and time problem as you acknowledged.