Physics 106P: Lecture 3 Notes · 2021. 2. 3. · V V V UNIVERSITY ... Imran Khan, Matt Wahila,...
Transcript of Physics 106P: Lecture 3 Notes · 2021. 2. 3. · V V V UNIVERSITY ... Imran Khan, Matt Wahila,...
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Lecture 6
Thermal Properties of Materials
o Heat Capacity o Thermal Conductivity o Thermal Expansion o Thermal Stresses
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Objectives
Explain the temperature dependence of heat capacity & thermal conductivity of metals and amorphous solids
Explain modes of heat transfer in metals and amorphous solids
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4.1 Heat Capacity (c)
C is a measure of ability of material to absorb thermal energy
C is measured as specific heat capacity, c (= Quantity of heat needed to cause unit temp rise in 1 kg of material)
C is measured under conditions of constant volume (Cv) or pressure (CP).
dT
dQC
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When a material is heated, the absorbed Thermal energy (dQ) increases the KE of the molecules thus raising the internal energy (U) of material.
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.U K E NRT N = Number of molecules
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)1..(....................3RdT
dU
dT
dQC
VV
V
Dulong Petit Law
For a constant volume process, the system does no work on the sorrounding i.e.,
By applying 1ST law of Thermodynamics, (dQ = dU + dW), Specific heat capacity at const volume (Cv) becomes (NB dW = 0)
( 0)dQ dU dW
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Temp Dependence of Heat Capacity
Eqn (1) Cv of solids is const. It is observed that
(i) Cv of solids obey Dulong petit law only at high T > D, where D = Debye temp.
(ii) As T 0, Cv T3 and fails to obey Dulong Petit Law
T
Cv Dulong Petit Law
Exp data for most solids
3R
D
D > room temp
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The Low temp behavior of Cv is explained using quantum theory – Einstein 1916
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Fig 1. Temp Dependence of Heat Capacity of materials
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Cv of Metals
Heat capacity of metals is due to contributions from phonons and electrons
Phonons are elastic waves that are emitted when atoms vibrate about their equilibrium positions. They travel at speed of sound
A phonon is a quantum of lattice vibrational wave with energy given by
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E
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Phonon contribution to Cv is ~ AT3 at T →
0K.
Electron contribution to Cv T and becomes significant (for metals only) as T → 0K.
Thus
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ho 3Metals P nons Elect
V V VC C C T T
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Cv of Ceramics
Compared to metals, ceramics have high specific heats and high MP due to strong bonds (mix of ionic & covalent) they can absorb a lot of heat and withstand high temps
Ceramics are used in high temp applications e.g., spark plugs
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6.2 Thermal Conductivity
It is a measure of the material’s ability to transmit heat from regions of high to low temperature.
Defined by
dx
heat
T2 T1
A
' .....(2)dT
Q K Fourier s Lawdx
o Q = Heat flux (Quantity of thermal energy flowing through a unit area per unit time)
o dT/dx = temperature gradient, k = Thermal conductivity
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Note the similarity of Eqn (2) to the Fick’s first law for atomic diffusion where the diffusion flux is concentration gradient:
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dx
dCDJ x
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Thermal Conductivity of Metals
K of metals is by a combination of phonons and electrons i.e.,
KMetals = Ke + KP
KP & Ke are phonon and electronic thermal conductivities.
Phonon conductivity is due to atomic vibrations while Electron conductivity is due to Free (conduction band) electrons
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Ke >> KP since electron mean free path >> phonon mean free path.
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Factors affecting K of metals
KMetals is affected by
(i) Impurities (Alloying) –This introduces scattering thereby reducing electron
mean free path Ke & KP reduces with increase in impurities
(ii) Temp:- Increase in temp increases scattering
Cu-Zn alloy
Wt% Zn
K
of
Cu
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T
metals
K
Metal melt &
Become
amorphous
800oC
Generally, KMetals 1/T
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Note:
Since free electrons are responsible for both electrical () and thermal conduction (K) in metals, the two conductivities are related to each other by the Wiedemann-Franz law:
where L = const
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T
KL
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Conductivity of non-metals
In crystalline solids (e.g NaCl) & amorphous solids (ceramics), thermal conductivity is due to phonons & occurs at 300K
At much higher T, phonon conductivity reduces due to increase in phonon scattering resulting from increased frequency of vibrations Kcryst 1/T.
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KCryst 1/T and KAmorp T
KMetals > KCrystalline > KCeramics.
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0 200 400(2K) 800 T(K)
Amorphous solids
Crystalline Solids & Dielectrics
K
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Ceramics lack the orderly lattice arrangements S.T Phonon transmission is interrupted by microstructural defects e.g., porosity, grain size & grain boundaries etc leading to low thermal conductivity compared to crystalline solids
KCeramics reduces with increase in structural defects
At very high temp, KCeramics increases due to radiant heat transfer (through pores)
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SEM of clay ceramics showing effect of Porosity on KCeramics (Photos Adapted from Nyongesa et al, 2002)
Grain boundaries reduces KCeramics
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Thermal Applications of ceramics
Ceramics are thermally insulative Used as insulators in high temp applications e.g.,
(ii) space shuttle
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(ii) Insulation in wall – using thin brick walls
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Research References
Ogacho A. A., Aduda B.O. and Nyongesa F.W., (2006). Thermal Shock Behaviour of a kaolinite refractory prepared using a natural organic binder., Journal of Material Science., 41, 8276 - 8283.
Ogacho A. A., Aduda B.O. and Nyongesa F.W., (2003). Thermal Conductivity of a Kaolinite Refractory; Effects of an Orgarnic Binder., Journal of Material Science., 38[11], 2293 - 2297.
(iii) Ceramic lining in “jikos” & furnaces – to
prevent heat loss
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4.3 Thermal Expansion
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The energy addition to a material in the form of heat increases the thermal vibration of the atoms in their lattice sites.
The thermal expansion is a direct result of a greater separation distance between the centers of adjacent atoms as the thermal vibration of individual atoms increases with increasing temperature.
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α for ceramics and glasses < α for metals due to the shape of the energy well.
The ceramics and glasses generally have deeper wells (higher bonding energies) due to their ionic and covalent bond natures; therefore less atomic separation with the increasing temperature.
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expansion thermal oft coefficienlinear ]./[ CmmmmLdT
dL o
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The elastic modulus is directly related to the derivative of the bonding energy curve near the bottom of the well. The deeper the well, the larger derivative and greater the elastic modulus.
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Linear thermal expansion coefficients of some ceramic oxides. [from W. D. Kingery]
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Front Row Left to Right: Junping Shao, Derek Stampone, Dan Clark, Francis Mutuku, Darshana Weerawarne, Joshua Hewlett, Jeremiah Dederick, Patrick OBrien Next Row standing Left to Right: Linda Wangoh, Imran Khan, Matt Wahila, Jonathan Li, Connor Harrison, Nick Quackenbush, Matt Gochan, Gavin Osterhoudt, Felix Sauoma, Ning Kang Last Row Standing, Left to Right: Calford Otieno, Greg Parks, Austin Faucett, Steve Button, Justin Leshen, Shawn Sallis, Faramarz Hadian, William Thompson.
Graduate Students- fall 2012- 2013
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6.4 Thermal Shock
Thermal shock: Fracture of materials due to differential contraction or expansion caused by sudden cooling/heating.
Thermal shock inducing surface cracks leading to failure
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1fR T
E
Capacity of material to withstand failure from Thermal Shock is called thermal Shock resistance (TSR)
TSR is defined by Hassleman parameters R, R’ and R’’’
= Measures Resistance of material to initiation of fracture by thermal shock = Min temp drop (T) necessary to produce fracture
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1f KR
E
= Measures of possibility
for crack propagation
2 1f
ER
= Measures ability of material to resist crack propagation
f = flexural strength, K = thermal conductivity
= coeff of thermal expansion, E = Elastic Modulus
= Poisson’s ratio, T = temp difference between material and quenchant temp
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Fig 1. TRS parameters vs “mrenda” binder concentration in kaolinite ceramics used in ceramic “jikos”
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Ogacho A., Aduda B., Nyongesa F.W., (2006)., J. Mater Sci., 41, 8276
Aduda B.O., Nyongesa F.W. and Njogu M. S., (2008)., J. Mater Sci., 43, 4107
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Activity
What can you infer from Fig 1?
What conclusions and recommendations can you draw from Fig 1?
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Fig 2. R′′′ vs Thermal Quench Cycles (N) for ceramic refractories made from various clay particle sizes
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• F. W. Nyongesa, N. Rahbar, S. K. Obwoya, J. Zimba, B. O. Aduda, and W.O. Soboyejo., (2011), ISRN Mech Eng, DOI 10.5402/2011/816853.
•N. Rahbar, S. K. Obwoya, J. Zimba, B. O. Aduda, F. W. Nyongesa, I. Yakub and W.O. Soboyejo., (2010)., Experimental Mechanics DOI 10.1007/s
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Activity
What can you infer from Fig 2?
What conclusions and recommendations can you draw from Fig 2?
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Examples of thermal shock failure
Teeth cracks when exposed to sudden temp gradient
Ceramic cooking stove cooled by pouring water will fail
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RESEACH REFERENCES
Ogacho A. A., Aduda B.O. and Nyongesa F.W., (2006). Thermal Shock Behaviour of a kaolinite refractory prepared using a natural organic binder., Journal of Material Science., 41, 8276 - 8283.
F. W. Nyongesa, N. Rahbar, S. K. Obwoya, J. Zimba, B. O. Aduda, and W.O. Soboyejo., (2011). An investigation of Thermal Shock in Porous Clay Ceramics, ISRN Mechanical Engineering, DOI 10.5402/2011/816853 – March 2011.
N. Rahbar, S. K. Obwoya, J. Zimba, B. O. Aduda, F. W. Nyongesa, I. Yakub and W.O. Soboyejo., (2010). Thermal Shock Resistance of a Kyanite-Based (Aluminosilicate) Ceramic, Experimental Mechanics DOI 10.1007/s – April 2010
Failure due to thermal shock can be prevented by increasing R’ through Increasing f and K
Decreasing thermal gradient by changing temperature slowly
Decreasing E
Increase Toughness trough toughening mechanisms
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Lecture -Evaluation
Explain why Cv is virtually independent of temp at temp far removed from 0K
Explain factors that influence thermal conductivity of metals & ceramics
Explain the temp dependence of thermal conductivity of Metals
Explain Thermal Shock and how to prevent failure from Thermal Shock