The Science and Engineering of Materials, 4th ed Donald R. Askeland

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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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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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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 25C. 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 25C. Higher melting
point metals tend to expand to a lesser degree.
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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 y-axis.
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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 950C.