1. Introduction to Materials Science and Engineering
Chapter 11: Thermal Properties
Textbook Chapter 20

2. Content Introduction Heat Capacity Thermal Expansion
Thermal Conductivity
5. Thermal Stress

3. Introduction 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?

4. Introduction:
In the mid-1800s, Mayer, Helmholtz, and Joule discovered independently that heat is simply a form of energy.
1853: Wiedemann and Franz law (good electrical conductors are generally good thermal conductors)
The ratio between heat conductivity and electrical conductivity (divided by the temperature) is essentially constant for all metals
The thermal conductivity only varies within four orders of magnitude while the electrical property varies about 25 orders of magnitude. (Fig. 18.1) – phonons, or lattice vibration quanta (Einstein)

5. Heat in physics is defined as energy transferred by thermal interactions. Heat flows spontaneously from systems of higher temperature to systems of lower temperature. When two systems come into thermal contact, they exchange energy through the microscopic interactions of their particles. When the systems are at different temperatures, this entails spontaneous net flow of energy from the hotter to the cooler, so that the hotter decreases in temperature and the cooler increases in temperature. This will continue until their temperatures are equal. Then the net flow of energy has settled to zero, and the systems are said to be in a relation of thermal equilibrium. Spontaneous heat transfer is an irreversible process.
The first law of thermodynamics states that the internal energy of an isolated system is conserved. To change the internal energy of a system, energy must be transferred to or from the system. For a closed system, heat and work are the mechanisms by which energy can be transferred. For an open system, internal energy can be changed also by transfer of matter.[6] Work performed by a body is, by definition, an energy transfer from the body that is due to a change to external or mechanical parameters of the body, such as the volume, magnetization, and location of center of mass in a gravitational field.[2][7][8][9][10][11]
When a body is heated, its internal energy increases. This additional energy is stored as kinetic and potential energy of the atoms and molecules in the body. [12] Heat itself is not stored within a body. Like work, it exists only as energy in transit from one body to another or between a body and its surroundings.
(from wikipedia)

6. Heat, Work, And Energy First law of thermodynamics
In this chapter, We limit our consideration to processes for which W can be considered to be Zero.
Energy, work, and heat have same unit.
1 cal = J
1 J = cal

7. Content Introduction Heat Capacity Thermal Expansion
Thermal Conductivity
5. Thermal Stress

8. Heat Capacity C'
Heat capacity : the amount of heat which needs to be transferred to a substance in order to raise its temperature by a certain temperature interval.
Generally, it is interested in two kinds : at constant volume & at constant pressure
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.
at constant V
at constant P
H=E+PV
These relationship is….

9. Specific Heat Capacity, c
Specific heat capacity is the heat capacity per unit mass
Molar Heat Capacity, cv
Molar heat capacity is the heat capacity per mole

10. Heated materials have the thermal energy
참고자료
Heated materials have the thermal energy
How is the thermal energy stored?
In the case of a water molecule

11. Solid : constrained vibration
참고자료
Monatomic gas: translation
Diatomic gas : translation, rotation, vibration
Liquid : translation, rotation, vibration
Solid : constrained vibration
vibration frequency  1012/sec
→ Energy Storing Mechanism

12. Heat Capacity vs T • Heat capacity... Cv T (K) • Atomic view:
-- 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 vibration

13. ©2003 Brooks/Cole, a division of Thomson Learning, Inc
©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

14. Energy Storage How is the energy stored?
Phonons – thermal waves - vibrational modes

15. 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

16. Specific Heat of Tungsten
How much heat must be supplied to 250 g of tungsten to raise its temperature from 25oC to 650oC?
If no losses occur, 5000 cal (or 20,920 J) must be supplied to the tungsten.

17. 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.
How can you make a rough estimation of specific heat?
→ Dulong Petit’s law : Cv = 3R ≈ 6 cal/mole oC ≈ 25 J/mole oC
The atomic weight of niobium is g/mol.
Thus the total heat required is:

18. Heat Capacity: Comparison
• Why is cp significantly
larger for polymers?
• 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

19. Content Introduction Heat Capacity Thermal Expansion
Thermal Conductivity
5. Thermal Stress

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

21. Correlation between Bonding Strength and Materials Properties
Melting Point
Elastic Modulus
Thermal-Expansion Coefficient

22. Properties from Bonding: a
Thermal expansion  asymmetric nature of the energy well
Broad well (generally more asymmetric)  larger expansion

23. 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 m
012 . )) C 9 ( 40 ) 15
)]( / 1 10 x 5 16 [ 6 = - D a l T o

24. Content Introduction Heat Capacity Thermal Expansion
Thermal Conductivity
5. Thermal Stress

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

26. 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

27. Which has the lowest thermal conductivity?
→ vacuum
Porosity in ceramic materials may have a dramatic
influence on thermal conductivity; increasing the pore
volume will, under most circumstances, result in
a reduction of the thermal conductivity.
Insulating properties of polymers are good but may
be further enhanced by the introduction of small pores,
which are ordinarily introduced by foaming during
polymerization. → foamed polystyrene
→ Styrofoam

28. Content Introduction Heat Capacity Thermal Expansion
Thermal Conductivity
5. Thermal Stress

29. Thermal Stress
Due to restrained thermal expansion and contraction

30. Thermal Stress
Due to temperature gradient

31. Thermal Stress • Occurs due to: • Example Problem 19.1, Callister 7e.
-- 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?

32. Thermal Shock Resistance
• 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.

33. Summary • A material responds to heat by: • Heat capacity:
-- 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.