The Science and Engineering
of Materials, 4th ed
Donald 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
21.2
21.3
21.4
Heat Capacity and Specific Heat
Thermal Expansion
Thermal Conductivity
Thermal Shock
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Section 21.1
Heat Capacity and Specific Heat
 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.
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Figure 21.1 Heat capacity as a function of temperature for
metals and ceramics.
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license.
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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Example 21.1
Specific Heat of Tungsten
How much heat must be supplied to 250 g of tungsten to raise
its temperature from 25oC to 650oC?
Example 21.1 SOLUTION
If no losses occur, 5000 cal (or 20,920 J) must be supplied to
the tungsten.
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Example 21.2
Specific Heat of Niobium
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 SOLUTION
The 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:
Thus the total heat required is:
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Section 21.2
Thermal Expansion
 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.
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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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Example 21.3
Bonding and Thermal Expansion
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?
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.
©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a
trademark used herein under license.
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Example 21.3 SOLUTION
Both 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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Example 21.4
Design of a Pattern for a Casting Process
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 SOLUTION
The 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:
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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Example 21.5
Design of a Protective Coating
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.
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Example 21.5 SOLUTION
If 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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Section 21.3
Thermal Conductivity
 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.
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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 yaxis.
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Example 21.6
Design of a Window Glass
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
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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Section 21.4
Thermal Shock
 Thermal shock - Failure of a material caused by stresses
introduced by sudden changes in temperature.
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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.
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