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

by klilly
Tags: melt
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klilly
#1
Sep19-11, 08:30 PM
P: 3
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 s1 m1 C1), how many hours will it take to melt all of the ice?
(Note: Lfwater = 3.35 105 J kg1)


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 :(
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issacnewton
#2
Sep19-11, 09:21 PM
P: 610
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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