A closed box is filled with dry ice at a temperature of -78.5^∘ C while the outside temperature

step 1 We have Q equals K a delta t over L. From here we can find that the thermal conductivity, k equa

A closed box is filled with dry ice at a temperature of...

A closed box is filled with dry ice at a temperature of $-78.5^{\circ} \mathrm{C}$ while the outside temperature is $21.0^{\circ} \mathrm{C} .$ The box is cubical, measuring 0.350 $\mathrm{m}$ on a side, and the thickness of the walls is $3.00 \times 10^{-2} \mathrm{m} .$ In one day, $3.10 \times 10^{6} \mathrm{J}$ of heat is conducted through the six walls. Find the thermal conductivity of the material from which the box is made.

Key Concepts

Thermal Conductivity

This is a material property that quantifies the ability of a substance to transfer heat through conduction. It is a measure of how quickly heat moves from a region of higher temperature to a region of lower temperature within the material, and it plays a crucial role in determining the rate of heat transfer.

Fourier’s Law of Conduction

Fourier’s Law provides the fundamental relation for the conduction process. It states that the rate of heat transfer through a material is proportional to the negative temperature gradient and the area perpendicular to the heat flow, with the proportionality constant being the thermal conductivity. This law is essential for setting up and solving conduction problems.

Temperature Gradient

This concept refers to the change in temperature per unit distance within a material. In conduction problems, the temperature difference between two surfaces divided by the thickness of the material creates a gradient that drives the heat transfer, and it is a key factor in calculating the rate of conduction using Fourier’s Law.

Geometric Factors in Heat Transfer

The physical dimensions of the object, such as surface area and thickness, are critical in heat transfer calculations. The area through which heat is conducted and the distance over which the temperature difference occurs (wall thickness in this case) directly influence the overall rate of heat transfer, as indicated in Fourier’s equation.

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