Responding to Temperature Changes

Abstract

Table 34.1 lists the important parameters we meet in this chapter and their units. The SI unit of temperature is kelvin (K), but as you have realized by now °C is often used in presenting data in materials science. As we mentioned in Chapter 1, the numerical value of a temperature difference or temperature interval expressed in °C is equal to the numerical value of the same temperature difference or interval when expressed in K. This point is worth remembering when you compare coefficients of thermal expansion or thermal conductivities for different materials.

1 People and History

Debye, Petrus (Peter) Josephus Wilhelmus (1884–1966) was born in The Netherlands and became a naturalized American citizen in 1946. In 1912, he proposed the idea of quantized elastic waves, called phonons. From 1940 to 1952 Debye was Professor of Chemistry at Cornell University. He won the Nobel Prize in Chemistry in 1936.

Thomson, William (Lord Kelvin) (1824–1907) Scottish mathematician and physicist born in Belfast, Ireland. He proposed his absolute scale of temperature in 1848. During his lifetime he published more than 600 papers and was elected to the Royal Society in 1851. He is buried in Westminster Abbey next to Isaac Newton.

2 Exercises

• 34.1 Why do we use this title rather than the usual “Thermal Properties”?

• 34.2 Show that equation 34.4 gives energy in units of J.

• 34.3 The melting temperature of MgO is 3,073 K, whereas that of NaCl is 1,074 K. Explain the reason for this difference.

• 34.4 Consider the structure of graphite. Would you expect the thermal conductivity to be the same parallel to the basal plane and perpendicular to the basal plane? If not, why not?

• 34.5 (a) Would you expect the thermal conductivity of crystalline quartz to be higher or lower than that of fused quartz? (b) Would you expect the differences in ${k}$ to increase or decrease with increasing temperature? Explain the reasoning behind your answers.

• 34.6 Using the criteria given in Section 34.5, rank the following ceramics in order of increasing thermal conductivity: B₄C, UO₂, TiO₂, and Si₃N₄. Explain the reasoning for your ranking.

• 34.7 Why is thermal transfer by radiation important only at high temperatures?

• 34.8 An AlN ceramic substrate contains 0.05 vol% porosity. Calculate the thermal conductivity of the ceramic at room temperature.

• 34.9 Which has the greater effect on the thermal conductivity of an AlN ceramic: 0.05 vol% porosity or 0.5 vol% of an Y₃Al₅O₁₂ second phase?

• 34.10 Would hot pressing or reaction bonding be the best method to produce Si₃N₄ components for applications in which sudden changes in temperature occur? Explain how you arrived at your answer.

• 34.11 Would the alkali alumina borosilicate glass given in Section 34.12 be a good choice to glaze a mullite crucible? If not, would you be better off using a soda-lime–silicate glaze or a pure silica glaze?

• 34.12 Use “book values” to compare the numerical heat capacities of the four ceramics in Figure 34.1. How can it rise above 3R?

• 34.13 The box on page 644 gives values for ${v}$ and ${l}$ for a ceramics and a metal. Why are they so different?

• 34.14 Explain why there is a variation in the data >800 K in Figure 34.3. Why there is a sharp maximum in this curve at low temperature?

• 34.15 Explain why the curves in Figure 34.4 are different for each material. Are there any trends? What materials would be been used to obtain these curves? Explain your reasoning.

• 34.16 What conclusions can you deduce from the plot of $\alpha$ versus ${T}$ in Figure 34.11?

• 34.17 The thermal expansion coefficients in Figure 34.12 all increase with temperature. Discuss what this means. In rare cases $\alpha$ can be negative. How can this happen, and could the phenomenon have useful applications?

• 34.18 What can you deduce from Figure 34.18? This requires real thought!

• 34.19 Zerodur is used at the Paranal Observatory. Could a similar material be used for the platter of a hard drive instead of glass? Explain your reasoning carefully.

• 34.20 Imagine you deposit a thin film of rock salt-structured oxide A (lattice parameter ${a}$) on a substrate of oxide B (lattice parameter 1.1${a}$) at 700°C. You then find that the thin film is in tension when it cools to room temperature. Explain what is happening.