How Long Will It Take for Ice to Melt in a Styrofoam Cooler?

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SUMMARY

The discussion centers on calculating the time required for 5.0 kg of ice at 0°C to melt in a Styrofoam cooler with a surface area of 1.0 m² and a thickness of 2.5 cm, under an external temperature of 35°C. The initial calculations using the thermal conductivity equation were incorrect due to misinterpretation of temperature change. The correct approach involves applying the latent heat equation, which accounts for the energy required to change the state of the ice without changing its temperature. The final calculation indicates that the time required for all the ice to melt is significantly less than the initially estimated 104.4 hours.

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  • Understanding of thermal conductivity and the equation kA(delta)T/d = Q/(delta)T
  • Knowledge of latent heat and its role in phase changes
  • Basic principles of heat transfer and conduction
  • Familiarity with specific heat capacity calculations
NEXT STEPS
  • Research the latent heat of fusion for ice and its application in phase change calculations
  • Learn about thermal conductivity coefficients for various materials, including Styrofoam
  • Explore detailed examples of heat transfer calculations in different geometries
  • Study the impact of surface area on heat transfer rates in thermal systems
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Homework Statement


A large styrofoam cooler has a surface area of 1.0m^2 and a thickness of 2.5cm. If 5.0kg of ice at 0C is stored inside and the outside temperature is a constant 35C, how long does it take for all the ice to melt? (Consider conduction only)


Homework Equations


kA(delta)T/d = Q/(delta)T

Q=mc(delta)T


The Attempt at a Solution


I tried (.042J/mxsxC)(1.0m^2)(35C)/.025m = 58.8j/s but I don't think that the change in temperature is correct.

But after getting that answer solve for Q=(5.0kg)(2100J/kgxC)(35C) = 367500J again i don't think the change in temperature is correct

Then divide 367000J/58.8j/s = 104.4 hours. which i know is incorrect

Help would be appreciated thanks
 
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The cube has 6 surfaces. So the area should be 6.0m^2.
 
the total surface area is 1.0m^2. But I figured it out, I just needed to use the latent heat equation
 

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