Materials Engineering (Week 5) Flashcards
Why Study Thermal Properties of
Materials?
Materials susceptible to thermal shock
brittle fracture from internal stress
due to cooling
Or, fracture from thermal gradients across coatings
E.g. Case Study 1 (Jet engine turbine blades)
- Function of thermal and mechanical properties
Coefficient of thermal expansion, thermal conductivity,
elasticity, fracture strength
Heat Capacity:
General: The ability of a material to absorb heat
Quantitative: The energy required to increase the
temperature of the material.
Heat Capacity Equation:
C = dQ / dT
C, heat capacity (J/mol - K)
dQ, energy input (J/mol)
dT, Temperature change (K)
Two ways to measure heat capacity: (2)
Cp : Heat capacity at constant pressure.
Cv : Heat capacity at constant volume.
Cp > Cv
Specific heat has typical units of
J / kg x K
Energy Storage
How is the (thermal) energy stored?
Phonons – thermal waves - vibrational modes
Energy Storage
Debye temperature:
linked to highest
frequency of phonons
(usually less than Troom )
Heat Capacity vs T
Heat capacity increases with what ?
Temp
SHC reaches a limiting value of 3R (R, gas constant)
Cv= AT^3 at low temp
Heat Capacity vs T
Atomic view:
– Energy is stored as atomic vibrations.
– As T goes up, so does the avg. energy of atomic vibr.
Heat Capacity: Comparison between metals and ceramics
Ceramics tend to have much higher SHC when compared to metals
Energy Storage
* Other small contributions to energy storage
– Electron energy levels
* Contribution is relatively large in metals at low
temperature.
Thermal Expansion
Materials change size when heating
Thermal Expansion
Equation
L(final) - L(initial) / L(initial) = alpha x (Tfinal -Tinitial)
L, length
alpha, coefficient of thermal expansion (1/K or 1/°C)
Thermal Expansion
Atomic View
Atomic view: Mean bond length increases with T.
bond energy vs bond length
curve is “asymmetric”
Thermal Expansion: Comparison
Is different for each element in both metals and ceramics
What is Thermal Conductivity
General: The ability of a material to transfer heat.
Thermal Conductivity: Equation
Fourier’s Law
q = -k (dT / dx)
q, heat flux, (J/m2-s)
k, thermal conductivity (J/m-K-s)
dT / dx, temperature gradient
Thermal Conductivity
Atomic View:
Atomic view: Atomic vibrations in hotter region carry
energy (vibrations) to cooler regions.
k = ke + kl
e – electronic, l - lattice k - thermal conductivity
Thermal Conductivity: Comparison of energy transfer for metals and ceramics
Which type of material have a higher thermal Conductivity
Metals: By vibration of atoms and motion of electrons
Ceramics: By vibration of atoms
Metals have much higher Thermal Conductivity
Explain the Thermal Conductivity trend for Ceramics
Intially decreases because of phonon scattering. Then
increases because of radiative heat transfer.
Thermal Stress, occurs due to what? (2)
– uneven heating/cooling
– mismatch in thermal expansion.
A material responds to heat by: (2)
– increased vibrational energy
– redistribution of this energy to achieve thermal equil.
Heat capacity: (2)
– energy required to increase a unit mass by a unit T.
– metals somewhat higher than ceramics.
Coefficient of thermal expansion: (2)
– the stress-free strain induced by heating by a unit T.
– metals higher than ceramics.
Thermal conductivity: (2)
– the ability of a material to transfer heat.
– metals have the largest values
Thermal shock resistance: (1)
– the ability of a material to be rapidly cooled and not
crack. Maximize sigma(f) k/E(alpha).
