1. Chapter 19: Thermal Properties
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?

2. Scientists do stupid looking things sometimes (though not too unsafe if they made the material carefully enough)

3. Heat Capacity temperature of the material.
• 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.
Cp > Cv
• Specific heat has typical units of

4. Heat Capacity vs T -- increases with temperature
-- reaches a limiting value of 3R
Adapted from Fig. 19.2, Callister 7e.
gas constant 3R
= 8.31 J/mol-K
Cv = constant
Debye temperature
(usually less than T
room )
T (K) q D Cv
• Atomic view:
-- Energy is stored as atomic vibrations.
-- As T goes up, so does the avg. energy of atomic vibr.

5. Energy Storage How is the energy stored?
Phonons – thermal waves - vibrational modes
Adapted from Fig. 19.1, Callister 7e.

6. Energy Storage Other small contributions to energy storage
Electron energy levels
Dominate for ceramics & plastics
Energy storage in vibrational modes
As energy increases the atoms vibrate faster & increase the bond distance
Adapted from Fig. 19.3, Callister 7e.

7. Heat Capacity: Comparison
• Why is cp significantly
larger for polymers?
Selected values from Table 19.1, Callister 7e.
• Polymers
Polypropylene
Polyethylene
Polystyrene
Teflon c p
(J/kg-K)
at room T
• Ceramics M
agnesia (MgO)
Alumina (Al 2 O 3 )
Glass
• Metals
Aluminum
Steel
Tungsten
Gold
1925
1850
1170
1050
900
486
138
128 : C
: (J/mol-K)
material
940
775
840
increasing c p

8. Thermal Expansion coefficient of Bond energy Bond length (r)
• Materials change size when heating. T
init
final L
coefficient of
thermal expansion (1/K or 1/°C)
• Atomic view: Mean bond length increases with T.
Adapted from Fig. 19.3(a), Callister 7e. (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.)
Bond energy
Bond length (r)
increasing T T 1
r(T5)
r(T1) 5
bond energy vs bond length
curve is “asymmetric”

9. Thermal Expansion: Comparison
Polypropylene
Polyethylene
Polystyrene
90-150
Teflon
• Polymers
at room T
• Ceramics
Magnesia (MgO)
13.5
Alumina (Al2O3)
7.6
Soda-lime glass 9
Silica (cryst. SiO2)
0.4
• Metals
Aluminum
23.6
Steel 12
Tungsten
4.5
Gold
14.2
a(10-6/K)
Material
Selected values from Table 19.1, Callister 7e.
Polymers have smaller  because of weak secondary bonds
• Q: Why does a
generally decrease
with increasing
bond energy?

10. Thermal Expansion: Example
Ex: A copper wire 15 m long is cooled from 40 to -9°C. How much change in length will it experience?
Answer: For Cu
rearranging Eqn 19.3b

11. Thermal Conductivity Fourier’s Law T T > T 1 2 1 x x 1 2
• General: The ability of a material to transfer heat.
• Quantitative:
temperature
gradient
Fourier’s Law
heat flux
(J/m2-s)
thermal conductivity (J/m-K-s) T T
> T 1 2 1 x x 1
heat flux 2
• Atomic view: Atomic vibrations in hotter region carry
energy (vibrations) to cooler regions.

12. Thermal Conductivity: Comparison
k (W/m-K)
Energy Transfer
Material
increasing k
• Metals
Aluminum
247
Steel 52
Tungsten
178
Gold
315
By vibration of
atoms and
motion of
electrons
• Ceramics
Magnesia (MgO) 38
Alumina (Al2O3) 39
Soda-lime glass
1.7
Silica (cryst. SiO2)
1.4
By vibration of
atoms
• Polymers
Polypropylene
0.12
Polyethylene
Polystyrene
0.13
Teflon
0.25
By vibration/
rotation of chain
molecules
Selected values from Table 19.1, Callister 7e.

13. THERMAL CONDUCTIVITY
Good heat conductors are usually good electrical conductors.
(Wiedemann & Franz, 1853)
Metals & Alloys: free e- pick up energy due to thermal vibrations of atoms as T increases and lose it when it decreases.
Insulators (Dielectrics): no free e-. Phonons (lattice vibration quanta) are created as T increases, eliminated as it decreases.

14. Thermal conductivity optimization
To maximize thermal conductivity, there are several options:
Provide as many free electrons (in the conduction band) as possible
free electrons conduct heat more efficiently than phonons.
Make crystalline instead of amorphous
irregular atomic positions in amorphous materials scatter phonons and diminish thermal conductivity
Remove grain boundaries
gb’s scatter electrons and phonons that carry heat
Remove pores (air is a terrible conductor of heat)

15. Thermal Stress -- uneven heating/cooling
• Occurs due to:
-- uneven heating/cooling
-- mismatch in thermal expansion.
• Example Problem 19.1, Callister 7e.
-- A brass rod is stress-free at room temperature (20°C).
-- It is heated up, but prevented from lengthening.
-- At what T does the stress reach -172 MPa? T
room L DL
100GPa
20 x 10-6 /°C
20°C
Answer: 106°C
-172 MPa
compressive  keeps L = 0

16. Thermal Shock Resistance (TSR)
• Occurs due to: uneven heating/cooling.
• Ex: Assume top thin layer is rapidly cooled from T1 to T2: s
rapid quench
resists contraction
tries to contract during cooling T2 T1
Tension develops at surface
Temperature difference that
can be produced by cooling:
Critical temperature difference
for fracture (set s = sf)
set equal
• Result:
• Large thermal shock resistance when is large.

17. Thermal Protection System
reinf C-C
(1650°C)
Re-entry T
Distribution
silica tiles
( °C)
nylon felt, silicon rubber
coating (400°C)
• Application:
Space Shuttle Orbiter
Chapter-opening photograph, Chapter 23, Callister 5e (courtesy of 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 )
• Silica tiles ( C):
--large scale application
--microstructure:
~90% porosity!
Si fibers
bonded to one
another during
heat treatment.
100 mm
Fig. 19.3W, Callister 5e. (Fig. 19.3W courtesy the National Aeronautics and Space Administration.)
Fig. 19.4W, Callister 5e. (Fig W courtesy Lockheed Aerospace Ceramics
Systems, Sunnyvale, CA.)

18. 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.
• 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 sf k/Ea.