A Styrofoam box has a surface area of 0.80 m^2 and a wall thickness of 2.0 cm . The temperature

step 1 A styrofoam box is a surface area of 0 .8 square meters and a wall thickness of 2 centimeters. T

A Styrofoam box has a surface area of 0.80 m^2 and a wall...

A Styrofoam box has a surface area of 0.80 $\mathrm{m}^{2}$ and a wall thickness of 2.0 $\mathrm{cm} .$ The temperature of the inner surface is $5.0^{\circ} \mathrm{C},$ and the outside temperature is $25^{\circ} \mathrm{C}$ . If it takes 8.0 $\mathrm{h}$ for 5.0 $\mathrm{kg}$ of ice to melt in the container, determine the thermal conductivity of the Styrofoam.

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Key Concepts

Latent Heat of Fusion

Latent heat of fusion is the amount of thermal energy required to change a substance from one phase (solid) to another phase (liquid) without changing its temperature. It represents the energy required to overcome the molecular forces during a phase change and is essential in energy balance calculations involving melting.

Fourier’s Law of Heat Conduction

Fourier's law relates the heat transfer rate through a material to the thermal conductivity, the area normal to heat flow, the temperature difference across the material, and inversely to the thickness of the material. It is the fundamental principle used to analyze conduction problems.

Thermal Conductivity

Thermal conductivity is a physical property of a material that indicates its ability to conduct heat. It is defined in Fourier's law and is used to calculate the rate at which heat passes through a material; higher conductivity means that heat is transferred more readily.

Heat Conduction

Heat conduction is the process by which thermal energy is transferred within or between substances due to a temperature gradient. It occurs at the molecular level where energetic particles transfer energy through collisions, and it is described quantitatively by Fourier's law.

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