Thermal Properties of Materials.pdf with clear

thermal properties

1. Properties of Materials

3. Why study the thermal properties of materials?
•Materials selection decisions for components that are exposed
to elevated temperatures and temperature changes

•Design engineer requires the understanding of the thermal
responses of materials, as well as access to the thermal
properties of a wide variety of materials.
Thermal property- the response of a material to the application of heat

•Heat capacity, thermal expansion, and thermal conductivity
are thermal properties of solids.

4. •Heat is a form of energy resulting from the motion between
particles of matter
What is heat ?
•Temperature measures the intensity of heat but also is related
to the degree of motion between particles of matter.

5. Heat capacity (C)
•Represents the amount of energy required to produce a unit temperature
rise.
•Indicative of material’s ability to absorb heat from the external surroundings.

•Mathematical terms, heat capacity of a material is the amount of energy
required to raise the temperature of a particular material in 1
0
K
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=
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�??????

Units : J/K

6. Specific heat capacity (c)
Specific heat capacity, often simply called specific heat, which is the heat
capacity per unit mass of a material.
Units : J/(Kg.K)
•Sometimes the heat capacity is specified as volume-specific heat capacity,
commonly called volumetric heat capacity, which is the heat capacity per
unit volume

7. Q
in
no W
out
•There two types of heat capacity, depends on the way in which the heat is transferred
according to environmental conditions
Heat capacity at constant volume
When heat is supplied to a system at constant volume, the
system is unable to do any work

8. dTCdQ
V
 Thus the supplied heat energy cause to increase only the internal energy of the
system
Where C
v is known as the heat capacity at constant volume V
V
T
Q
C 








Constant volume

9. Q
in
W
out
Heat capacity at constant pressure
If heat is supplied to a substance at constant pressure, it is free to expand doing
work against the constant pressure
•A part of the heat supplied to the system is utilized for the work expansion
and more heat will be required to raise the temperature than that required
in a constant volume process for the same temperature change.

10. •The amount of heat required is related to temperature rise as dTCdQ
p

Constant pressure
•Where Cp is called the heat capacity at constant pressure. Thus, p
p
T
Q
C 








•Since for a given temperature change, the heat required is more in a
constant pressure process than that in a constant volume process, C
p > C
v

•However, the difference between C
p and C
v for solid and liquid are very
small compared to that for gases, as the change in volume of solids and
liquids during is not very significant

11. •Atoms in solid materials are constantly vibrating at very high frequencies and with
relatively small amplitudes.
•A single quantum of vibrational energy is called
a phonon which is analogous to the quantum of
electromagnetic radiation, the photon.
•These elastic waves also participate in the
transport of energy during thermal conduction.
•These vibrations are coordinated in such a
way that lattice waves are produced which
propagate through the crystal at the velocity
of sound.
Figure 01: Schematic representation of the generation of
lattice waves in a crystal by means of atomic vibrations

12. Specific heat capacity
(J/kg K)

Aluminum 900

Steel 486
Tungsten 138
Gold 128
Specific heat capacity comparison (room temperature values)
Metals Ceramics
Specific heat capacity
(J/kg K)

Alumina (Al
2O
3) 775

Magnesia (MgO) 940
Glass 840
Polymers
Specific heat capacity
(J/kg K)

Polypropylene 1925

Polyethylene 1850

Polystyrene 1170
Teflon 1050
Why is c
significantly larger for
polymer?
•Covalent bond in polymers do
not let atoms exchange
electrons like metallic bonds
do

13. Example 01: Estimate the energy required to raise the temperature of 5 kg of the aluminum,
aluminum oxide(alumina) and polypropylene materials from 20 to 150 °C.
Specific heat capacities of aluminum, aluminum oxide(alumina) and polypropylene are 900, 775 and
1925 J/kg K respectively.  
kgm
kgKJc
KKdT
5
/900
130)27320()273150(



Specific heat capacity �=
�??????
�.�??????

Energy required �??????=�.�.�??????
= 900 J/kg K x 5 kg x130 K
= 585 kJ
??????�??????�??????�??????�
??????�??????�??????�??????
Energy required �??????=�.�.�??????
= 775 J/kg K x 5 kg x130 K
= 503.75 kJ

14. Polypropylene
Energy required �??????=�.�.�??????
= 1925 J/kg K x 5 kg x130 K
= 1251.25 kJ

15. Thermal expansion of materials
•Most solid materials expand upon heating and contract on cooling.
•The change in length with temperature for a solid material may be expressed
as:
Where, and are initial and final length after temperature increases from
initial to final
α
l= Linear coefficient of thermal expansion (°C
-1
)

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??????
??????
??????
=??????
1??????
�−??????
?????? or
??????
??????
�
??????
∆�
�
??????
=??????
�∆??????
�
�
??????
�
�
�
�
??????
??????
??????
??????
�
Material α
l values (°C
-1
)

Metals 5-25 x 10
-6
Ceramics 0.5-15 x 10
-6

Polymers 50-400 x 10
-6

16. α
l values (10
-6
°C
-1
)

Aluminum 23.6

Steel 12
Tungsten 4.5
Gold 14.2
Coefficient of Thermal Expansion comparison (room temperature values)
Metals Ceramics
α
l values (10
-6
°C
-1
)

Alumina (Al
2O
3) 7.6

Magnesia (MgO) 13.5
Glass 9
Silica (Cryst. SiO
2) 0.4
Polymers
α
l values (10
-6
°C
-1
)

Polypropylene 145-180

Polyethylene 106-198

Polystyrene 90-150
Teflon 126-216
•Polymers have larger α
1 values because of weak secondary
bonds.

•Linear and branched polymers expand more because the
secondary intermolecular bonds are weak, and there is
minimum cross linking.

•Lower coefficients are found in thermosetting network
polymers in which the bonding is almost entirely covalent.

17. Thermal expansion of materials
•Temperature of solid is a measure of its potential energy.
•Heating to successively higher temperatures raises the vibrational energy.
•The greater the atomic bonding energy, the deeper
and more narrower this potential energy trough.
•Thus the interatomic separation increases from r
0 to r
1
to r
2 and so on. (r
0-equilibrium interatomic spacing at
0K-trough minimum point)
•Thus, the increase in interatomic separation with a
given rise in temperature will be lower yielding a small
value of linear co-efficient of thermal expansion (α
f)
Potential energy trough
•Thermal expansion is an result of asymmetric curvature of
potential energy trough, rather than the increased atomic
vibrational amplitudes with rising temperature.

18. Example 02: A 0.4 m rod of a metal elongates 0.48 mm on heating from 20 to
100 °C. Determine the value of the linear coefficient of thermal expansion
for this material.
∆�
�??????
=??????
�∆?????? mxl
ml
CT
i
3
0
1048.0
4.0
80)20100(



 ??????
�=
∆�
�??????∆??????

??????
�=
�.�????????????��
−
�
�
�.� � ?????? ??????� °??????

??????
�=
�.�????????????��
−
�
�
�.� � ?????? ??????� °??????

Linear coefficient of thermal expansion ??????
�=15 x 10
-6 0
C
-1

19. Example 03: A bimetallic strip is constructed from strips of two different
metals that are bonded along their lengths. Explain how such a device may
be used in a thermostat to regulate temperature.
Bimetallic strip consists of two strips of different metals which
expand at different rates as they are heated, usually steel and
copper, or in some cases steel and brass.
The strips are joined together throughout their length by
riveting, brazing or welding.
The different expansions force the flat strip to bend one way if
heated, and in the opposite direction if cooled below its initial
temperature.
The metal with the higher coefficient of thermal expansion is
on the outer side of the curve when the strip is heated and on
the inner side when cooled.

20. Thermal conductivity of materials
•It is common knowledge that some materials such as metals conduct heat
readily, whereas others such as wood act as thermal insulators.
•The physical property that describe the rate at which heat is conducted is
the thermal conductivity (K)
•Heat conduction in fluids can be though of as molecular energy transport.
Mechanism is the motion of the constituent molecules. For solid materials,
heat is transported by free electrons and by vibrational lattice waves or
phonons.
•When a temperature gradient exist in a stationary medium, which may
be a solid or a fluid, we use the term conduction to refer to the heat
transfer that will occur across the medium.

21. Fourier’s Law of Heat Conduction
•The rate of heat transfer can be quantify by Fourier’s law which states that for steady state, the
heat flux is directly proportional to temperature gradient.
•For the one dimensional plane wall having a temperature distribution T(x), the rate equation is
expressed as dx
dT
kq
x

"
The constant K is a transport property known as the thermal
conductivity. (W/m.k)
Here q”
x is a heat flux, that is , the rate of heat of
transfer per unit area
T(X)
T
2
T
1
q(x)
x
y
L
Negative sign indicates that heat flows in the
direction of decreasing temperature

22. •Thermal conduction in solid takes place by both lattice vibration waves
(phonons) and free electrons. Thus total conductivity is
•Metals are extremely good conductors of heat because relatively large
numbers of free electrons exist that participate in thermal conduction.
•The purest form of metal will have
high conductivity than the alloy form
•In the alloy different atom will have
different electron affinity, thus
movement of excited electrons
becomes hard.
�=�
??????+�
�
Metals
Material Thermal conductivity
W/m.K)

Silver 410

Copper 385
Gold 314
Aluminum 210
Iron 80
Steel 52

23. •They are thermal insulators are they lack charge numbers of free electrons.
•Thus, the phonons are primarily responsible for thermal conduction (�
&#3627408466;<&#3627408472;
??????)
•The room temperature thermal conductivities range between approximately 2-
50 W/m-K
Ceramics
•Also, the phonon are not as effective as free electrons in the transport of heat
energy due to phonon scattering by lattice imperfections.
•Amorphous ceramics have lower conductivities than crystalline ceramics as
atomic structure is highly disordered and irregular
•Higher porosity also reduces conductivity due to presence of still air (0.02
W/m-K) in pores

24. •Energy transfer is accomplished by the vibration and rotation of the chain
molecules.
•Magnitude of the thermal conductivity depends on the degree of crystallinity
•Thermal conductivities for most polymers are of the order of 0.3 W/m-K
Polymers
•Highly crystalline and ordered structure - means effective coordinated
vibration- higher thermal conductivity

25. k (W/m-K)

Aluminum 247

Steel 52
Tungsten 178
Gold 315
Thermal conductivity comparison (room temperature values)
Metals Ceramics
k (W/m-K)

Alumina (Al
2O
3) 39

Magnesia (MgO) 38
Glass 1.7
Silica (Cryst. SiO
2) 1.4
Polymers
k (W/m-K)
Polypropylene 0.12

Polyethylene 0.46-0.5

Polystyrene 0.13
Teflon 0.25
•Energy transfer mechanism-Atomic
vibrations and motion of free electrons
•Energy transfer mechanism-Atomic vibrations
•Energy transfer mechanism-
vibration/rotation of chain molecules

26. Example 04: (a) Calculate the heat flux through a sheet of brass 7.5 mm thick if the
temperatures at the two faces are 150 and 50°C ; assume steady-state heat flow.

(b) What is the heat loss per hour if the area of the sheet is 0.5 m
2 dx
dT
kq
x

"  
mxdx
KmWk
KKdT
3
105.7
/120
100)27350()273150(



 mx
K
Km
W
q
x 3
"
105.7
100
120

 mx
K
Km
W
q
x 3
"
105.7
100
120

 2
6"
106.1
m
W
xq
x

(a)Heat flux through a sheet

27. (b) heat loss per hour, area of the sheet is 0.5 m
2
2
2
6'
5.0106.1 mx
m
W
xqtransferheatofrate
x
 Wx
6
108.0 hrJx
hr
Jx
lossheat /1088.2
3600
1
108.0
9
6




28. Example 05: Briefly explain why metals are typically better thermal conductors
than ceramic materials.
In metals, energy is transferred by atomic vibrations and motion of free electrons.

But in ceramics heat transfer is occurred due to the atomic vibrations only.

Therefore thermal conduction of metals is higher than ceramic materials.