Engineering 45
Thermal
Properties
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Learning Goals – Thermal Props
 Learn How Materials Respond to
Elevated Temperatures
 How to Define and Measure
•
Heat Capacity and/or Specific Heat
•
Coefficient of Thermal Expansion
•
Thermal Conductivity
•
Thermal Shock Resistance
 How Ceramics, Metals, and Polymers
rank in Hi-Temp Applications
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Heat Capacity (Specific Heat)
 Concept  Ability of a Substance to
Absorb/Supply Heat Relative to its
Change in Temperature
 Quantitatively
heat capacity
(J/mol-K)
dQ
C
dT
energy input (J/mol or J/kg)
temperature change (K)
 C typically Specified by the Conditions of the
Measurement
• Cp → Constant PRESSURE on the Specimen
• Cv → Specimen Held at Constant VOLUME
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Measure Specific Heat
 Recall from ENGR43
Battery
q or w  VI  t
• Where
– q & w  Heat or
Work or Energy
(Joules or Watt-Sec)
– V  Electrical Potential
(Volts)
– I  Electrical Current
(Amps)
– t  time sec
Insulation
  The specific Heat for a Solid at Rm-P
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Measure Specific Heat cont
dQ q m VI  t m
cp 


dT
T
T f  Ti
 To Find cp, Measure
• Block Mass, m (kg)
• Voltage, V (Volts)
Battery
Insulation
• Current, I (Amps)
• Initial Temperature,
Ti (K or °C)
• Final Temperature, Tf
(K or °C)
• Run Time, t (s)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Specific Heats Compared
 cp and C for Some Common Substances At 298K
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Cp vs Cv Measurements
 GASES are Almost
Always Measured at
Constant VOLUME
• e.g., Fill a Sealed
container with Silane
(SiH4) Add Heat, and
Measure T
 Solids & Liquids
Typically Measured
at Constant
PRESSURE
Engineering-45: Materials of Engineering
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• Set the Solid or
Liquid-Container on
the table at
ATMOSPHERIC
Pressure (101.325
kPa), Add Heat &
Measure T
 Example = Co
E = 208.6 GPa
100 mm
 = 0.31
 = 1.3×10-5 K-1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Cp or Cv for Co
 = 0.31
 Heat the Block
by 20K
 = 1.3×10-5 K-1
 Then the Change in
Volume, V


5

V  100mm  1.3 10 / K  20 K

3
V  0.026mm  1.758 10 5 mm3
3
 V V  1.756 10 11  17.56 ppT
 A VERY Small
Difference
Engineering-45: Materials of Engineering
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100 mm
E = 208.6 GPa
 The HydroStatic (allover) Stress Required
to Maintain constant V
E V V 

31  2 


208.6 109 Pa 1.756 10 11

31  2  0.31
  3.21Pa 0.003% of an ATM 
• Very Hard to Control to
Maintain Const-V
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Cv as Function of Temperature
 Cv
• Increases with Increasing T
• Tends to a limiting Value of 3R = 24.93 J/mol-k
 Quantitatively
3R=24.93
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Cv as Function of Temp cont
 For Many Crystalline
Solids
Cv  AT 3 : T  TD
Cv  Cv , HiT  C p
 const : T  TD
• Where
– A  Material
Dependent
CONSTANT
– TD  Debye
Temperature, K
Engineering-45: Materials of Engineering
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 Atomic Physics
• Energy is Stored in
Lattice Vibration Waves
Called Phonons
– Analogous to Optical
PHOTONS
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
increasing cp
Cp Comparison
cp (J/kg-K)
material
at room T
• Polymers
1925
Polypropylene
cp: (J/kg-K)
1850
Polyethylene
Cp: (J/mol-K)
1170
Polystyrene
1050
Teflon
• Ceramics
Magnesia (MgO) 940
• Why is cp significantly
Alumina (Al2O3)
775
larger for polymers?
Glass (SiO2)
840
• Metals
Aluminum
Steel
Tungsten
Gold
Engineering-45: Materials of Engineering
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900
486
128
138
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
4
Thermal Expansion
 Concept  Materials Change Size When Heated
Tinit
L final  Linit
Linit
  T final  Tinit
Tfinal
Linit


Lfinal
Coefficient of Thermal Expansion
• T↑  E↑
• ri is at the
Statistical Avg of
the Trough Width
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increasing T
r(T1)
r(T5)
  due to Asymmetry of Bond energy
PE InterAtomic Distant
Trough
T5
T1
Bond length (r)
Bond-energy vs
bond-length
curve is “asymmetric
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Thermal Expansion: Comparison
increasing 
Material
at room T
• Polymers
145-180
Polypropylene
106-198
Polyethylene
90-150
Polystyrene
126-216
Teflon
• Metals
Aluminum
23.6
Steel
12
Tungsten
4.5
Gold
14.2
• Ceramics
Magnesia (MgO)
13.5
Alumina (Al2O3)
7.6
Soda-lime glass
9
Silica (cryst. SiO2)
0.4
Engineering-45: Materials of Engineering
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 (10 -6 /K)
• Q: Why does 
generally decrease
with increasing
bond energy?
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
6
Thermal Conductivity
 Concept  Ability of a Substance Tranfer Heat
Relative to Temperature Differences
 Quantitatively, Consider a Cold←Hot Bar
T2 > T1
T1
x1
x2
heat flux
 Characterize the Heat Flux as
heat flux
(W/m2)
dT
q  k
dx
• Q: Why the
NEGATIVE Sign
before k?
thermal conductivity (W/m-K)
Engineering-45: Materials of Engineering
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temperature
Gradient (K/m)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Thermal Conductivity: Comparison
Material
• Metals
k (W/m-K)
increasing k
Aluminum
Steel
Tungsten
Gold
247
52
178
315
By vibration of
atoms and
motion of
electrons
38
39
1.7
1.4
By vibration of
atoms
• Ceramics
Magnesia (MgO)
Alumina (Al2O3)
Soda-lime glass
Silica (cryst. SiO2)
• Polymers
Polypropylene
Polyethylene
Polystyrene
Teflon
Engineering-45: Materials of Engineering
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Energy Transfer
By vibration/
0.12
0.46-0.50 rotation of chain
molecules
0.13
0.25
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Thermal Stresses
 As Noted Previously a Material’s Tendency to
Expand/Contract is Characterized by α
 If a Heated/Cooled Material is Restrained to
its Original Shape, then Thermal Stresses will
Develop within the material
 For a Solid Material
  E l / lo 
• Where
–
–
–
–
  Stress (Pa or typically MPa)
E  Modulus of Elasticity; a.k.a., Young’s Modulus (GPa)
l  Change in Length due to the Application of a force (m)
lo  Original, Unloaded Length (m)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Thermal Stresses cont.
 From Before
l / lo   T 
 Sub l/l into Young’s Modulus Eqn To
Determine the Thermal Stress Relation
  E T 
 Eample: a 1” Round 7075-T6 Al
(5.6Zn, 2.5Mg, 1.6Cu, 0.23Cr wt%’s)
Bar Must be Compressed by a 8200 lb
force when restrained and Heated
from Room Temp (295K)
• Find The Avg Temperature for the Bar
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Thermal Stress Example
 Find Stress
F 8200lb
8200lb
 

2
A d 4  1in 2 4
F
   10 440 psi  72MPa
A
 Recall the Thermal
Stress Eqn
  E T 
0 lbs
8200 lbs
 E = 10.4 Mpsi
= 71.7 GPa
 α = 13.5 µin/in-°F
= 13.5 µm/m-°F
 Need E & α
• Consult Matls Ref
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Thermal Stress Example cont
 Solve Thermal
Stress Reln for ΔT
T   E
0 lbs
8200 lbs
72 106 Pa
T 
71.7 109 Pa 13.5 10 6 /  F
T  74.4 F  41.3K
 Since The Bar was Originally at Room Temp
T f  Ti  T
T f  297  41  338 K
T f  65C  150 F
Engineering-45: Materials of Engineering
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• Heating to Hot-Coffee
Temps Produces Stresses
That are about 2/3 of the
Yield Strength (15 Ksi)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
Thermal Shock Resistance
 Occurs due to: uneven heating/cooling.
 Ex: Assume top thin layer is rapidly cooled from T1 to T2:
rapid quench
tries to contract during cooling T2
doesn’t want to contract

T1
Temperature difference that
can be produced by cooling:
quenchrate
(T1  T2 ) 
k
Tension develops at surface
  E (T1  T2 )
Critical temperature difference
for fracture (set  = f)
f
(T1  T2 ) fracture 
E
set equal
fk
 TSR
• Result: (quenchrate) for fracture 
E
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
TSR – Physical Meaning
fk
 The Reln TSR 
E
 For Improved (GREATER) TSR want
• f↑  Material can withstand higher
thermally-generated stress before fracture
• k↑  Hi-Conductivity results in SMALLER
Temperature Gradients; i.e., lower ΔT
• E↓ More FLEXIBLE Material so the thermal stress
from a given thermal strain will be reduced (σ = Eε)
• α↓  Better Dimensional Stability; i.e., fewer
restraining forces developed
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt
WhiteBoard Work
 Problem 19.5 – Debye Temperature
Charles Kittel, “Introduction to Solid State
Physics”, 6e, John Wiley & Sons, 1986. pg-110
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-13_Thermal_Props.ppt