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

[klilly]

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

Homework Statement

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)

Homework Equations

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

The Attempt at a Solution

Answer is: 56 hours
I have no idea how to get to this :(

 

[issacnewton]

law of thermal conduction says

$$\mathcal{P}=kA\;\frac{\Delta T}{\Delta x}$$

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

$$Q=m_{ice}L_f$$

m_ice=2 kg ; L_f=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