Thermal properties of materials including heat capacity, thermal expansion, conductivity, and stresses are important considerations in engineering. Heat capacity is a measure of how much energy is required to change a material's temperature. Thermal expansion describes how a material increases in size with increasing heat. Thermal conductivity determines how quickly heat transfers through a material. Thermal stresses occur due to temperature differences and constraints, which can cause cracking or deformation. Understanding these thermal properties aids engineering design for withstanding various temperature conditions and stresses.

1. Ethiopian Institute of Technology-Mekelle
Mekelle University, Ethiopia
December, 2019
School of Mechanical and Industrial
Engineering
Manufacturing Engineering Chair
Department of material science
Advanced engineering materials and
processing
Heat capacity, thermal properties, expansions,
conductivity and stress
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2. introduction
 Thermal Properties. Thermal ... linear and volume
coefficients of thermal expansion ... Heat capacity is a
measure of the ability of the material to ....
Thermal conductivity: heat is transferred from high to low ....
At what temperature does the stress reach -172 MPa? T. 0
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3. How heat creates on materials
 Light, electrical, mechanical, chemical, nuclear, sound
and thermal energy itself can each cause a substance
to heat up by increasing the speed of its molecules.
 So, put energy into a system and it heats up, take energy away
and it cools. ...
 So, when you heat something up, you are just making its
molecules move faster.
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4. Heat
 Heat is a form of energy called thermal energy which flows
from a higher temperature body to a lower temperature body
when they are placed in contact.
 Heat or thermal energy of a body is the sum of kinetic energies
of all its constituent particles, on account of translational,
vibrational and rotational motion.
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5. Cont.
 The SI unit of heat energy is joule (J).
 The practical unit of heat energy is calorie.
 1 cal. = 4.18 J
 1 calorie is the quantity of heat required to
raise the temperature of 1 g of water by 1°C.
 Mechanical energy or work (W) can be
converted into heat (Q) by 1 W = JQ 5

6. 6
J = Joule’s mechanical equivalent of heat.
J is a conversion factor (not a physical quantity) and
its value is 4.186 J/cal.
Cont.
where

7. Heat capacity
 Heat capacity is a material’s ability to absorb heat from the
external surroundings; it represents the amount of energy
needed to increase the temperature of a substance 1 degree, so
the units are J / oC. In mathematical terms, the heat capacity C
is expressed as follows: C = ΔQ/ΔT = dQ/dT [J/deg] Where
dQ is the energy required to produce a dT temperature change.
Ordinarily, heat capacity is specified per mole of material (e.g.,
J/mol-K, or cal/mol-K). Table below give the heat capacity of
some materials. When the temperature is increased, the kinetic
energy of the particles in the material changes. 7

8. Heat capacity of various
materials (at RT)
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9. Cont.…….
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10. Temperature
 Temperature of a body is the degree of hotness or coldness of
the body.
 A device which is used to measure the temperature is called a
thermometer.
 Branch of Physics dealing with production and measurement
temperature close to 0 K is known as cryogenics,
 while that deaf with the measurement of very high temperature
is called pyromet
 NTP or STP implies 273.15 K (0°C = 32°F).
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11. Different Scale of
Temperatures
1. Celsius Scale in this scale of temperature, the melting point
ice is taken as 0°C and the boiling point of water as 100°C
2. Fahrenheit Scale in this scale of temperature, the melt point
of ice is taken as 32°F and the boiling point of water as 211
3. Kelvin Scale in this scale of temperature, the melting pouxl
ice is taken as 273 K and the boiling point of water as 373 K
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12. Relation between Different Scales of
Temperatures
Specific Heat
 The amount of heat required to raise the temperature of unit
mass the substance through 1°C is called its specific heat.
 It is denoted by c or s.
 Its SI unit is joule/kilogram-°C'(J/kg-°C).
 Its dimensions are [L2T-2θ-1].
 The specific heat of water is 4200 J kg-1°C-1 or 1 cal. g-1
C-1, which high compared with most other substances.
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13. Gases have two types of specific heat
i. The specific heat capacity at constant volume (Cv).
ii. The specific heat capacity at constant pressure (Cr).
 Specific heat at constant pressure (Cp) is greater than specific
heat constant volume(CV), i.e., Cp > CV.
 For molar specific heats Cp – CV = R
where
 R = gas constant and this relation is called Mayer’s formula.
 The ratio of two principal specific heats of a gas is represented
by γ.
 The value of depends on atomicity of the gas.
 Amount γ of heat energy required to change the temperature of
any substance is given by Q = mcΔt 13

14. Cont.
where, m = mass of the substance = specific heat of the
substance and Δt = change in temperature.
Thermal Expansion
Is a process which increases the size material by heating is called
thermal expansion. There are three types of thermal expansion.
 Expansion of solids
 Expansion of liquids
 Expansion of gases
Expansion of Solids
Three types of expansion -takes place in solid. these are
1. Linear Expansion, 2. Superficial Expansion and 3. Cubical
Expansion 14

15. Linear Expansion
Linear Expansion is an expansion in length material by heating
is called linear expansion.
 And the mathematical expression of a linear expansion
Increase in length are L2 = L1(1 + α Δt)
where,
• L1 and L2 are initial and final lengths,
• Δt = change in temperature and
• α = coefficient of linear expansion.
 Coefficient of linear expansion expressed as α = (Δl/l * Δt)
 where 1= real length and Δl = change in length and Δt=
change in temperature 15

16. Superficial Expansion
Superficial Expansion is an Expansion in area on heating
is called superficial expansion. Increase in area A2 = A1(1 +
β Δt)
where,
• A1 and A2 are initial and final areas and
• β is a coefficient of superficial expansion.
• Coefficient of superficial expansion β = (ΔA/A * Δt)
where.
• A = area,
• ΔA = change in area and
• Δt = change in temperature
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17. Cubical Expansion
Cubical Expansion is an expansion in volume on
heating is called cubical expansion. Increase in
volume V2 = V1(1 + γ Δ t)
where
• V1 and V2 are initial and final volumes and
• γ is a coefficient of cubical expansion.
 Coefficient of cubical expansion
where
• V = real volume,
• ΔV =change in volume and
• Δ t = change in temperature.
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18. Cont..
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Relation between coefficients of linear, superficial and
cubical expansions
β = 2α and γ = 3α or α: β: γ = 1:2:3

19. Expansion of Liquids
Expansion of Liquids In liquids only expansion in volume takes
place on heating.
1. Apparent Expansion of Liquids When expansion of the
container containing liquid, on heating is not taken into
account then observed expansion is called apparent
expansion of liquids.
Coefficient of apparent expansion of a liquid
1. Real Expansion of Liquids When expansion of the
container, containing liquid, on heating is also taken into
account, then observed expansion is called real expansion of
liquids. 19

20. Cont.…
 Coefficient of real expansion of a liquid
 Both, yr, and ya are measured in °C-1. We can show that
 yr = ya + yg
where,
• yr, and ya are coefficient of real and apparent expansion of
liquids and
• yg is coefficient of cubical expansion of the container
 Anomalous Expansion of Water When temperature of water
is increased from 0°C, then its vol. decreases up to 4°C,
becomes minimum at 4°C and then increases.
 behavior of water around 4°C is called, anomalous expansion water. 20

21. Expansion of Gases
Expansion of Gases There are two types of coefficient of
expansion in gases
 Volume Coefficient (γv) At constant pressure, the change in
volume per unit volume per degree Celsius is called volume
coefficient.
where
 V0, V1, and V2 are volumes of the gas at 0°C, t1°C and t2°C.
 Pressure Coefficient (γp) At constant volume, the change in
pressure per unit pressure per degree Celsius is called pressure
coefficient.
where
 P0, P1 and P2 are pressure of the gas at 0°C, t1°C and t2°C.
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22. Thermal Conductivity.
Thermal conductivity refers to the amount/speed of heat
transmitted through a material. Heat transfer occurs at a higher
rate across materials of high thermal conductivity than those of
low thermal conductivity. ...
Thermal conductivity of materials is temperature dependent.
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23. Resistances of thermal conductivity
materials
 These phenolic resin insulation materials have characteristic
flame resistance, low smoke generation, low thermal
conductivity, and high temperature resistance. Phenolic resin
foams are good heat insulators up to 120°C, whereas glass
wool and rock wool are good insulators up to 260°C and 385
°C, respectively.
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24. Thermal stresses
 Thermal stress is stress caused by differences
in temperature or by differences
in thermal expansion. A crack formed as a
result of thermal stress produced by rapid
cooling from a high temperature. Because the
section of rail was fixed at both ends it
experienced a thermal stress when the
ambient temperature increased.
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25. Effects of thermal stresses on
materials
 Thermal stress is stress created by any change in temperature
to a material. These stresses can lead to fracture or plastic
deformation depending on the other variables of heating,
which include material types and constraints.
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26. Protections of thermal stress
 Thermal protection system (TPS) materials are used to
manufacture the heat shield that protects the structure, the
aerodynamic surfaces, and the payload of missiles and
warheads
 from the severe heating encountered during the entry flight
through a planetary
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27. conclusions
In generally
 the thermal properties
 Heat capacity
 Thermal expansion
 Thermal conductivity&
 Thermal stresses of materials are under thermodynamics
engineering's
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