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Erubus
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Homework Statement
A styrofoam cooler is in the shape of a rectangular box. Its interior dimensions are 30×40×60 cm. Its walls are 1.5 cm thick. It contains 4.0 kg of ice with the remaining space filled with water. The ice and water are in thermal equilibrium. The outside temperature is 25◦C, the coefficient of heat transfer for styrofoam is 0.023 W/m·K, and the latent heat of fusion for ice is 330kJ/kg. How long will it take for all the ice to melt?
(Answer: 8.9 hours)
Homework Equations
Q = L*Δm
[itex]\frac{dQ}{dt}[/itex] = [itex]\frac{kA}{l}[/itex]*(T1- T2)
The Attempt at a Solution
Since the inside is a mixture of water and ice, the internal temperature is 0°C.
I use the latent heat equation because the inside is only going through a phase change.
I set the two equations equal to each other so that:
[itex]\frac{kA}{l}[/itex]*(T[itex]_{outside}[/itex] - 0) = L*[itex]\frac{dMass}{dt}[/itex]
and changing it so I can take an integral:
dM = [itex]\frac{kA}{l*L}[/itex](T[itex]_{outside}[/itex])dt
[itex]\int^{0}_{4}[/itex]dM = [itex]\frac{kA}{l*L}[/itex](T[itex]_{outside}[/itex])[itex]\int[/itex]dt
but the integral doesn't work out because integrating from the initial mass of the ice (4kg) to the final (0kg) ends up as ln(-4)
I think I set up the two equations incorrectly at the start.