Calculate how long it will take for the ice to melt?

  1. Sep 19, 2011 #1
    Calculate how long it will take for the ice to melt??

    1. The problem statement, all variables and given/known data

    A chilly bin has walls 5.90 cm thick and the total area of the walls is 0.700 m2. The chilly bin is loaded with 2.00 kg of ice at 0.00 °C and stood on a rack so that its entire surface is in contact with the air. The temperature on the outside of the chilly bin is 28.0 °C. If the chilly bin is made of styrofoam (kstyrofoam = 0.0100 J s–1 m–1 °C–1), how many hours will it take to melt all of the ice?
    (Note: Lfwater = 3.35 × 105 J kg–1)


    2. Relevant equations

    I was given (L (water) x m (water))/ kA(Change in T/Change in thickness)
    But it didnt work out right


    3. The attempt at a solution

    Answer is: 56 hours
    I have no idea how to get to this :(
     
  2. jcsd
  3. Sep 19, 2011 #2
    Re: Calculate how long it will take for the ice to melt??

    law of thermal conduction says

    [tex]\mathcal{P}=kA\;\frac{\Delta T}{\Delta x}[/tex]

    where P is the power transferred, k is thermal conductivity, A is the area of the surface through which energy will flow, [itex]\frac{\Delta T}{\Delta x}[/itex] is temperature gradient.
    [itex]\Delta T[/itex] is the temperature difference between inner and outer surface,
    [itex]\Delta x[/itex] is the thickness of the bin.

    now we have been given , for chilly bin (made out of styrofoam)

    k= 0.0100 J s-1 m-1 °C-1
    A=0.700 m2
    delta T=28-0=28 °C
    delta x=5.92 x 10-2 m

    using this you can find the power which transfers from the outside to inside where ice is
    stored. P= 3.322 J s-1=3.322 W

    now amount of energy required to melt m kg of ice is

    [tex]Q=m_{ice}L_f[/tex]

    mice=2 kg ; Lf=3.35 × 105 J kg-1

    so we get Q= 6.7 x 105 J

    if t is the time required to melt all ice then Q must be equal to P x t . solve for t. its 56 hrs
     
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