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(Rate of Heat Flow)

  1. Oct 5, 2014 #1
    1. The problem statement, all variables and given/known data

    The same question was asked on this forum about two years ago, however I did not find any of the given answers clear. The question was the following:

    A small pond has a layer of ice 1cm thick floating on its surface. The air temperature is -10C.

    (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?

    2. Relevant equations

    H = dQ/dt = kA(TH - TC)/L

    3. The attempt at a solution

    for part b, I attempted to derive H with respect to L, and got the following:

    dH/dL = -kA(TH - TC)/L2

    I am not sure if I am misunderstanding what the question wants from me, and would appreciate any guidance anyone provides.
     
  2. jcsd
  3. Oct 5, 2014 #2
    If A is the surface area and ##\Delta x## is the thickness of ice that gets frozen during the time interval ##\Delta t##, what volume of ice gets frozen during the time interval ##\Delta t##? What is the mass of ice that gets frozen during the time interval ##\Delta t##? How much heat has to be removed from the mass during the time interval ##\Delta t## to freeze this mass of ice?

    Chet
     
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