   Chapter 11, Problem 50P

Chapter
Section
Textbook Problem

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

To determine
The thermal conductivity of the Styrofoam box.

Explanation

Given Info: The surface area of the box is 0.80m2 , the thickness of the wall is 2.0cm , temperature of the inner surface is 5.0°C , temperature of the outer surface is 25°C , and the time taken to melt 5.0 kg of ice is 8.0 h.

The energy supplied melt the ice at 0°C .

Formula to calculate the rate of energy transfer into the Styrofoam box is,

P=QΔt

• P is the power delivered to the Styrofoam box,
• Q is the heat supplied in to the box,
• Δt is the duration of heat transfer,

Formula to calculate the heat delivered to the Styrofoam box is,

Q=miceLf

• mice is the mass of the ice melt,
• Lf is the latent heat of fusion of ice,

Use miceLf for Q in P=QΔt to rewrite P.

P=miceLfΔt

Formula to calculate the rate of energy conducted by the Styrofoam box is,

P=kA(ThTc)L

• P is the rate of energy conducted by the Styrofoam box,
• k is the thermal conductivity of Styrofoam,
• A is the area of the Styrofoam,
• Th is the outside temperature,
• Tc is the inside temperature,
• L is the thickness of the Styrofoam,

Equate both the rate of energy conducted equations and rewrite in terms of k.

miceLfΔt=kA(ThTc)Lk=(miceLfΔt)(LA(ThTc))

Substitute 5

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