Chapter 17: Thermal Properties

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A white-hot cube of a silica fiber insulation
material, which, only seconds after having been
removed from a hot furnace, can be held by its
edges with the bare hands. Initially, the heat
transfer from the surface is relatively rapid
however, the thermal conductivity of this
material is so small that heat conduction from
the interior maximum temperature approximately
1250C (2300F) is extremely slow. This material
was developed especially for the tiles that cover
the Space Shuttle Orbiters and protect and
insulate them during their fiery reentry into the
atmosphere. Other attractive features of this
high-temperature reusable surface insulation
(HRSI) include low density and a low coefficient
of thermal expansion.

• Chapter 17 Thermal Properties

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CHAPTER 17THERMAL PROPERTIES17.1
IntroductionThermal property Response of
materials to the application of heat
ISSUES TO ADDRESS...
How does a material respond to heat?
How do we define and measure... --heat
capacity --coefficient of thermal expansion
--thermal conductivity --thermal shock
resistance
How do ceramics, metals, and polymers rank?
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17.2 HEAT CAPACITY
General The ability of a material to absorb
heat. Quantitative The energy required to
increase the temperature of the material.
energy input (J/mol)
heat capacity (J/mol-K)
temperature change (K)
Two ways to measure heat capacity -- Cp
Heat capacity at constant pressure. -- Cv
Heat capacity at constant volume.
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Vibrational Heat Capacity Generation of lattice
waves in a crystal by atomic vibrations. The
phonon versus photon
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Heat Capacity vs T
--increases with temperature --reaches a limiting
value of 3R
Cv constant 3R
Atomic view --Energy is stored as atomic
vibrations. --As T goes up, energy of atomic
vibration goes up too
The temperature dependence of the heat capacity
at constant volume. qD Debye temperature qD
hnmax/k qD lt Troom
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HEAT CAPACITY COMPARISON
Why is cp significantly larger for
polymers?
Selected values from Table 19.1, Callister 6e.
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17.3 THERMAL EXPANSION
Materials change size when heating.
coefficient of thermal expansion (1/K)
Atomic view Mean bond length increases with
T.
Adapted from Fig. 19.3(a), Callister 6e. (Fig.
19.3(a) adapted from R.M. Rose, L.A. Shepard, and
J. Wulff, The Structure and Properties of
Materials, Vol. 4, Electronic Properties, John
Wiley and Sons, Inc., 1966.)
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Potential energy versus interatomic distance.
Interatomic separation increases with rising
temperature. With heating, the interatomic
separation increases from r0 to r1 to r2, and so
on.
For a symmetric potential energy-versus-interatomi
c distance curve, there is no increase in
interatomic separation with rising temperature
(i.e., r1 r2 r3).
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THERMAL EXPANSION COMPARISON
Q Why does a generally decrease
with increasing bond energy?
Selected values from Table 19.1, Callister 6e.
For thermal expansion of fractional volume For
isotropic materials av 3al
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17.4 THERMAL CONDUCTIVITY
General The ability of a material to
transfer heat. Quantitative
temperature gradient
heat flux (J/m2-s)
thermal conductivity (J/m-K-s)
Atomic view Atomic vibrations in hotter
region carry energy (vibrations) to cooler
regions.
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THERMAL CONDUCTIVITY
Selected values from Table 19.1, Callister 6e.
for pure metals
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Thermal conductivity versus composition for
copperzinc alloys.
Impurities decrease thermal conductivity
(scattering centers in solid solutions)
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Dependence of thermal conductivity on temperature
for ceramics
Nonmetallic materials Thermal insulators Phonons
for thermal conduction Phonon scattering by
imperfections At higher T, radiant heat
transfer Porosity increasing pore volume
reduces thermal conductivity also gaseous
convection ineffective
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17.5 Thermal StressesREVIEW OF ELASTIC PROPERTIES
Modulus of Elasticity, E (also known as
Young's modulus)
Hooke's Law
s E e
E GPa or psi
s E e

• s stress
• E modulus of elasticity
• displacement

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17.5 THERMAL STRESSES
Occurs due to --uneven heating/cooling
--mismatch in thermal expansion.
Example --A brass rod is stress-free at
room temperature (20C). --It is heated up,
but prevented from lengthening. --At what T
does the stress reach -172 MPa?
100GPa
20 x 10-6 /C
20C
Answer 106C
-172MPa
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THERMAL SHOCK RESISTANCE
Occurs due to uneven heating/cooling. Ex
Assume top thin layer is rapidly cooled from T1
to T2
Tension develops at surface
Critical temperature difference for fracture (set
s sf)
Temperature difference that can be produced by
cooling
set equal
Result
Large thermal shock resistance when
is large.
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c17tf01
c17tf01
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THERMAL PROTECTION SYSTEM
Application
Space Shuttle Orbiter
Fig. 23.0, Callister 5e. (Fig. 23.0 courtesy the
National Aeronautics and Space Administration.
Fig. 19.2W, Callister 6e. (Fig. 19.2W adapted
from L.J. Korb, C.A. Morant, R.M. Calland, and
C.S. Thatcher, "The Shuttle Orbiter Thermal
Protection System", Ceramic Bulletin, No. 11,
Nov. 1981, p. 1189.)
Silica tiles (400-1260C)
--large scale application
--microstructure
90 porosity! Si fibers bonded to one another
during heat treatment.
Fig. 19.3W, Callister 5e. (Fig. 19.3W courtesy
the National Aeronautics and Space Administration.
Fig. 19.4W, Callister 5e. (Fig. 219.4W courtesy
Lockheed Aerospace Ceramics Systems, Sunnyvale,
CA.)
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Low expansion alloys
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SUMMARY
A material responds to heat by
--increased vibrational energy
--redistribution of this energy to achieve
thermal equil. Heat capacity --energy
required to increase a unit mass by a unit T.
--polymers have the largest values.
Coefficient of thermal expansion --the
stress-free strain induced by heating by a unit
T. --polymers have the largest values.
Thermal conductivity --the ability of a
material to transfer heat. --metals have the
largest values. Thermal shock resistance
--the ability of a material to be rapidly cooled
and not crack. Maximize sfk/Ea.
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Heat Capacity To what temperature would 10 lbm of
a brass specimen at 25C (77F) be raised if 65
Btu of heat is supplied? Solution We are asked
to determine the temperature to which 10 lbm of
brass initially at 25C would be raised if 65 Btu
of heat is supplied. This is accomplished by
utilization of a modified form of Equation 17.1 as
CdQ/dT c(1/m) dQ/dT
in which DQ is the amount of heat supplied, m is
the mass of the specimen, and cp is the specific
heat. From Table 17.1, cp 375 J/kg-K for
brass, which in Customary U.S. units is just
Thus
and
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• Briefly explain why Cv rises with increasing
  temperature at temperatures near 0 K.
• Briefly explain why Cv becomes virtually
  independent of temperature at temperatures far
  removed from 0 K.
• Solution
• (a) Cv rises with increasing temperature at
  temperatures near 0 K because, in this
  temperature range, the allowed vibrational energy
  levels of the lattice waves are far apart
  relative to the available thermal energy, and
  only a portion of the lattice waves may be
  excited. As temperature increases, more of the
  lattice waves may be excited by the available
  thermal energy, and, hence, the ability of the
  solid to absorb energy (i.e., the magnitude of
  the heat capacity) increases.
• (b) At temperatures far removed from 0 K, Cv
  becomes independent of temperature because all of
  the lattice waves have been excited and the
  energy required to produce an incremental
  temperature change is nearly constant.

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Thermal Expansion A copper wire 15 m (49.2 ft)
long is cooled from 40 to 9C (104 to 15F).
How much change in length will it
experience? Solution In order to determine the
change in length of the copper wire, we must
employ a rearranged form of Equation 17.3b and
using the value of al taken from Table 17.1 17.0
? 10-6 (C)-1 as
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Briefly explain why metals are typically better
thermal conductors than ceramic
materials. Solution Metals are typically
better thermal conductors than are ceramic
materials because, for metals, most of the heat
is transported by free electrons (of which there
are relatively large numbers). In ceramic
materials, the primary mode of thermal conduction
is via phonons, and phonons are more easily
scattered than are free electrons.
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For some ceramic materials, why does the thermal
conductivity first decrease and then increase
with rising temperature? Solution For some
ceramic materials, the thermal conductivity first
decreases with rising temperature because the
scattering of lattice vibrations increases with
temperature. At higher temperatures, the thermal
conductivity will increase for some ceramics that
are porous because radiant heat transfer across
pores may become important, which process
increases with rising temperature.
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For each of the following pairs of materials,
decide which has the larger thermal conductivity.
Justify your choices. (a) Fused silica
polycrystalline silica. (b) Atactic
polypropylene (
106 g/mol) isotactic polypropylene (
5 105 g/mol).
Solution (a) Polycrystalline silica will have
a larger conductivity than fused silica because
fused silica is noncrystalline and lattice
vibrations are more effectively scattered in
noncrystalline materials. (b) The isotactic
polypropylene will have a larger thermal
conductivity than the atactic polypropylene
because isotactic polymers have a higher degree
of crystallinity. Since heat transfer is
accomplished by molecular chain vibrations, and
the coordination of these vibrations increases
with percent crystallinity, the higher the
crystallinity, the greater the thermal
conductivity.
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What measures may be taken to reduce the
likelihood of thermal shock of a ceramic
piece? Solution According to Equation 17.9,
the thermal shock resistance of a ceramic piece
may be enhanced by increasing the fracture
strength and thermal conductivity, and by
decreasing the elastic modulus and linear
coefficient of thermal expansion. Of these
parameters, sf and al are most amenable to
alteration, usually be changing the composition
and/or the microstructure.