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The Science and Engineering of Materials, 4th edDonald R. Askeland – Pradeep P. Phulé

Chapter 21 – Thermal Properties of Materials

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Objectives of Chapter 21 To discuss heat capacity, thermal

expansion properties, and the thermal conductivity of materials.

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Chapter Outline 21.1 Heat Capacity and Specific Heat 21.2 Thermal Expansion 21.3 Thermal Conductivity 21.4 Thermal Shock

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Phonon - A packet of elastic waves. It is characterized by its energy, wavelength, or frequency, which transfers energy through a material.

Specific heat - The energy required to raise the temperature of one gram of a material by one degree.

Section 21.1 Heat Capacity and Specific Heat

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Figure 21.1 Heat capacity as a function of temperature for metals and ceramics.

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Figure 21.2 The effect of temperature on the specific heat of iron. Both the change in crystal structure and the change from ferromagnetic to paramagnetic behavior are indicated.

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How much heat must be supplied to 250 g of tungsten to raise its temperature from 25oC to 650oC?Example 21.1 SOLUTION

Example 21.1 Specific Heat of Tungsten

If no losses occur, 5000 cal (or 20,920 J) must be supplied to the tungsten.

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Suppose the temperature of 50 g of niobium increases 75oC when heated for a period. Estimate the specific heat and determine the heat in calories required.Example 21.2 SOLUTIONThe atomic weight of niobium is 92.91 g/mol. We can use Equation 21-3 to estimate the heat required to raise the temperature of one gram by one oC:

Example 21.2 Specific Heat of Niobium

Thus the total heat required is:

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Linear coefficient of thermal expansion - Describes the amount by which each unit length of a material changes when the temperature of the material changes by one degree.

Thermal stresses - Stresses introduced into a material due to differences in the amount of expansion or contraction that occur because of a temperature change.

Section 21.2 Thermal Expansion

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Figure 21.3 The relationship between the linear coefficient of thermal expansion and the melting temperature in metals at 25°C. Higher melting point metals tend to expand to a lesser degree.

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Figure 21.4 (a) The linear coefficient of thermal expansion of iron changes abruptly at temperatures where an allotropic transformation occurs. (b) The expansion of Invar is very low due to the magnetic properties of the material at low temperatures.

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Explain why, in Figure 21.3, the linear coefficients of thermal expansion for silicon and tin do not fall on the curve. How would you expect germanium to fit into this figure?

Example 21.3 Bonding and Thermal Expansion

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Figure 21.3 The relationship between the linear coefficient of thermal expansion and the melting temperature in metals at 25°C. Higher melting point metals tend to expand to a lesser degree.

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Example 21.3 SOLUTIONBoth silicon and tin are covalently bonded. The strong covalent bonds are more difficult to stretch than the metallic bonds (a deeper trough in the energy-separation curve), so these elements have a lower coefficient. Since germanium also is covalently bonded, its thermal expansion should be less than that predicted by Figure 21.3.

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Design the dimensions for a pattern that will be used to produce a rectangular-shaped aluminum casting having dimensions at 25oC of 25 cm 25 cm 3 cm.Example 21.4 SOLUTIONThe linear coefficient of thermal expansion for aluminum is 25 10-6 1/oC. The temperature change from the freezing temperature to 25oC is 660 - 25 = 635oC. The change in any dimension is given by:

Example 21.4 Design of a Pattern for a Casting Process

For the 25-cm dimensions, lf = 25 cm. We wish to find l0 :

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Example 21.4 SOLUTION (Continued)

For the 3-cm dimensions, lf = 3 cm.

If we design the pattern to the dimensions 25.40 cm 25.40 cm 3.05 cm, the casting should contract to the required dimensions.

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A ceramic enamel is to be applied to a 1020 steel plate. The ceramic has a fracture strength of 4000 psi, a modulus of elasticity of 15 106 psi, and a coefficient of thermal expansion of 10 10-6 1/oC. Design the maximum temperature change that can be allowed without cracking the ceramic.

Example 21.5 Design of a Protective Coating

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Example 21.5 SOLUTIONIf only the enamel heated (and the steel remained at a constant temperature), the maximum temperature change would be:

However, the steel also expands. Its coefficient of thermal expansion (Table 21-2) is 12 10-6 1/oC and its modulus of elasticity is 30 106 psi. The net coefficient of expansion is

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Thermal conductivity - A microstructure-sensitive property that measures the rate at which heat is transferred through a material.

Lorentz constant - The constant that relates electrical and thermal conductivity.

Section 21.3 Thermal Conductivity

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Figure 21.5 When one end of a bar is heated, a heat flux Q/A flows toward the cold ends at a rate determined by the temperature gradient produced in the bar.

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Figure 21.6 The effect of temperature on the thermal conductivity of selected materials. Note the log scale on the y-axis.

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Design a glass window 4 ft 4 ft square that separates a room at 25oC from the outside at 40oC and allows no more than 5 106 cal of heat to enter the room each day. Assume thermal conductivity of glass is 0.96 W . m-1 K-1 or 0.023 cal/cm . s . K.Example 21.6 SOLUTION

Example 21.6 Design of a Window Glass

where Q/A is the heat transferred per second through the window.

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Example 21.6 SOLUTION (Continued)

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Thermal shock - Failure of a material caused by stresses introduced by sudden changes in temperature.

Section 21.4 Thermal Shock

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Figure 21.7 The effect of quenching temperature difference on the modulus of rupture of sialon. The thermal shock resistance of the ceramic is good up to about 950°C.