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Chapter 19: Problem 19

For some ceramic materials, why does the thermal conductivity first decrease and then increase with rising temperature?

Short Answer

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Question: Explain why the thermal conductivity of some ceramic materials first decreases and then increases with rising temperature. Answer: The thermal conductivity of some ceramic materials initially decreases with rising temperature due to increased phonon-phonon scattering, which obstructs heat flow. At higher temperatures, the dominant heat transfer mechanism shifts from phonons to radiative processes, leading to an increase in thermal conductivity.

Step by step solution

01

Understand Thermal Conductivity

Thermal conductivity is a property of materials that represents their ability to conduct heat. It is denoted by the symbol 'k' and given in units of W/(m·K). The higher the value of thermal conductivity, the better a material is at transmitting heat.
02

Ceramics and their unique properties

Ceramics are inorganic, nonmetallic materials that are usually made from compounds of a metal and a non-metal. They have a crystalline structure, which gives them unique properties such as high hardness, low thermal conductivity, and high melting points.
03

Temperature dependence of thermal conductivity in ceramics

In ceramics, the thermal conductivity generally has a complex dependence on temperature. This is due to the combination of several heat transfer mechanisms like lattice vibrations (phonons), electronic contributions, and radiative contributions.
04

Decreasing thermal conductivity at low temperatures

At low temperatures, the main heat transfer mechanism in ceramics is through lattice vibrations (phonons). As the temperature increases, the phonon mean free path (the average distance a phonon can travel without scattering) decreases due to increased phonon-phonon scattering. This results in a decreased thermal conductivity, as there are more obstructions to the flow of heat.
05

Increasing thermal conductivity at high temperatures

As the temperature continues to increase, the dominant heat transfer mechanism in ceramics shifts from lattice vibrations to radiation. The increasing temperature leads to a higher thermal radiation contribution, and consequently, the overall thermal conductivity of the material starts to increase. In conclusion, the thermal conductivity of some ceramic materials initially decreases with rising temperature due to increased phonon-phonon scattering, and then increases at higher temperatures because of the shift in the dominant heat transfer mechanism from phonons to radiative processes.

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Most popular questions from this chapter

Briefly explain why the thermal conductivities are higher for crystalline than for noncrystalline ceramics.

The constant \(A\) in Equation \(19.2\) is \(12 \pi^{4} R / 5 \theta_{\mathrm{D}}^{3}\), where \(R\) is the gas constant and \(\theta_{\mathrm{D}}\) is the Debye temperature \((\mathrm{K})\). Estimate \(\theta_{\mathrm{D}}\) for aluminum, given that the specific heat is \(4.60 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) at \(15 \mathrm{~K}\).

Compute the density for iron at \(700^{\circ} \mathrm{C}\), given that its room- temperature density is \(7.870 \mathrm{~g} / \mathrm{cm}^{3} .\) Assume that the volume coefficient of thermal expansion, \(\alpha_{v}\), is equal to \(3 \alpha_{l}\).

For copper, the heat capacity at constant volume \(C_{v}\) at \(20 \mathrm{~K}\) is \(0.38 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\) and the Debye temperature is \(340 \mathrm{~K}\). Estimate the specific heat for the following: (a) at \(40 \mathrm{~K}\) (b) at \(400 \mathrm{~K}\)

Briefly explain thermal expansion using the poential energy-versus-interatomic spacing curve.
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