CHAPTER 17: THERMAL PROPERTIES ISSUES TO ADDRESS... • How does a material respond to heat? • How do we define and measure... --heat capacity --coefficient of thermal expansion --thermal conductivity --thermal shock resistance • How do ceramics, metals, and polymers rank? 1

Chapter 17 – Thermal Properties Motivation Many applications necessitate a thorough understanding of how materials respond to temperature changes How does a material respond to heat? Much of this will be a refresher for you (especially if you have taken/are taking heat transfer)! End of lecture 1

HEAT CAPACITY • General: The ability of a material to absorb heat. • Quantitative: The energy required to increase the temperature of the material. energy input (J/mol) heat capacity (J/mol-K) temperature change (K) • Two ways to measure heat capacity: -- Cp : Heat capacity at constant pressure. -- Cv : Heat capacity at constant volume. 2

Vibrational Heat capacity Chapter 17 – Thermal Properties Vibrational Heat capacity In most solids the principal mode of heat absorption is by increasing the vibrational energy of the atoms Atoms are constantly vibrating at high frequencies Atomic vibrations are coupled because of bonding Waves have very high frequencies and short wavelengths, and travel at the velocity of sound From quantum mechanics – the vibrational energies must have well-defined (quantized) values A single quantum of vibration energy is called a phonon Tie to Ch 12 – the thermal scattering of free electrons during conduction is by phonons End of lecture 1

Vibrational contribution to heat capacity How does Cv vary with temperature? The heat capacity is zero at zero 0 K Strongly nonlinear below the Debye temperature Plateau above the Debye temperature

HEAT CAPACITY VS T • Heat capacity... • Atomic view: --increases with temperature --reaches a limiting value of 3R Adapted from Fig. 19.2, Callister 6e. • Atomic view: --Energy is stored as atomic vibrations. --As T goes up, so does the avg. energy of atomic vibr. 3

Chapter 17 – Thermal Properties Other heat capacity contributions Other mechanisms for heat absorption are possible, though are usually minor compared to the vibrational contribution Electronic contribution – electrons increase their KE with heat absorption (do you think this is significant?) Must be free electrons to contribute to this Randomization of spins in a ferromagnetic material produces heat at T > Curie temperature End of lecture 1

HEAT CAPACITY: COMPARISON • Why is cp significantly larger for polymers? Selected values from Table 19.1, Callister 6e. 4

THERMAL EXPANSION • Materials change size when heating. coefficient of thermal expansion (1/K) • Atomic view: Mean bond length increases with T. Adapted from Fig. 19.3(a), Callister 6e. (Fig. 19.3(a) adapted from R.M. Rose, L.A. Shepard, and J. Wulff, The Structure and Properties of Materials, Vol. 4, Electronic Properties, John Wiley and Sons, Inc., 1966.) 5

Chapter 17 – Thermal Properties Thermal expansion How does a sample’s length change upon heating/cooling? End of lecture 1 lf and lo are the final and initial lengths, al – linear coefficient of thermal expansion al [=] 1/K Could also express this in terms of volume Molecular picture – expansion is due to increase in spacing of atoms

Asymmetric curvature of the potential well The shape/depth of the potential well is related to bonding strength – stronger bonds, smaller al Increase of interatomic separation with increasing T

THERMAL EXPANSION: COMPARISON • Q: Why does a generally decrease with increasing bond energy? Selected values from Table 19.1, Callister 6e. 6

Thermal properties (relate to bonding strength) Chapter 17 – Thermal Properties Thermal properties (relate to bonding strength) Metals: al typically between 5 – 25 x 10-6 1/C Can make alloys with lower values Ceramics – low expansion coefficients (0.5–15 x 10-6 1/C); coefficient can be anisotropic Polymers – can have very high expansion coefficients End of lecture 1

THERMAL CONDUCTIVITY • General: The ability of a material to transfer heat. • Quantitative: temperature gradient Similar to Fick’s first law heat flux (J/m2-s) thermal conductivity (J/m-K-s) • Atomic view: Atomic vibrations in hotter region carry energy (vibrations) to cooler regions. 7

Chapter 17 – Thermal Properties Thermal conductivity Mechanism for transport of heat from high to low temperature domains q – heat flux (W/m2) k – thermal conductivity (W/m-K) Mechanisms of heat conduction Two contributions: lattice vibration waves (phonons) and free electrons End of lecture 1

Thermal conductivity in metals Free electron mechanism dominates (k ~ 20 – 400 W/m-K) Free electrons participate both in thermal and electrical conduction – Wiedemann-Franz law L is a constant

Effect of impurities on thermal conductivity

Chapter 17 – Thermal Properties Ceramics Very few free electrons … phonon processes dominate the heat conduction process (k ~ 2 – 50 W/m-K) Amorphous materials have lower thermal conductivities than crystalline solids (why?) Most ceramics conductivity goes down when temperature increases (why?) But at very high temperature, radiation takes place also Porosity leads to reduction (dramatic) in thermal conductivity (why?) Polymers k is small ~ 0.3 W/m-K Energy transfer due to vibration and rotation of the chains k depends on polymer crystallinity Typically viewed as thermal insulators End of lecture 1

THERMAL CONDUCTIVITY: COMPARISON Selected values from Table 19.1, Callister 6e. 8

Chapter 17 – Thermal Properties Thermal stresses Induced as a result of temperature changes Consider an isotropic solid rod heated or cooled uniformly; no T gradient imposed. However if the axial motion of the rod is restrained, introduces stress (think back to thermal expansion!) Magnitude of the stress is given by Stresses caused by temperature gradients: Heating – compressive stress Cooling – tensile stress End of lecture 1

EX: THERMAL STRESS • Occurs due to: --uneven heating/cooling --mismatch in thermal expansion. • Example Problem 17.1, p. 724, Callister 2e. --A brass rod is stress-free at room temperature (20C). --It is heated up, but prevented from lengthening (ends are kept rigid). --At what T does the stress reach -172MPa? 100GPa 20 x 10-6 /C 20C -172MPa Answer: 106C 9

Chapter 17 – Thermal Properties Thermal shock (brittle materials) So, change in temperature can cause stress If these are large enough can have plastic deformation (for metals) But brittle materials can’t deform plastically! Brittle materials can fracture due to large temperature changes (thermal shock) Cooling more problematic – why? This is a problem because ceramics are very good insulators How to know when thermal shock can happen – thermal shock resistance parameter End of lecture 1 High fracture strengths High thermal conductivities Low elasticity modulus Low coeff. thermal expansion

THERMAL SHOCK RESISTANCE • Occurs due to: uneven heating/cooling. • Ex: Assume top thin layer is rapidly cooled from T1 to T2: Tension develops at surface Temperature difference that can be produced by cooling: Critical temperature difference for fracture (set s = sf) set equal • Result: • Large thermal shock resistance when is large. 10

THERMAL PROTECTION SYSTEM • Application: Space Shuttle Orbiter Fig. 23.0, Callister 5e. (Fig. 23.0 courtesy the National Aeronautics and Space Administration. Fig. 19.2W, Callister 6e. (Fig. 19.2W adapted from L.J. Korb, C.A. Morant, R.M. Calland, and C.S. Thatcher, "The Shuttle Orbiter Thermal Protection System", Ceramic Bulletin, No. 11, Nov. 1981, p. 1189.) • Silica tiles (400-1260C): --large scale application --microstructure: ~90% porosity! Si fibers bonded to one another during heat treatment. Fig. 19.3W, Callister 5e. (Fig. 19.3W courtesy the National Aeronautics and Space Administration. Fig. 19.4W, Callister 5e. (Fig. 219.4W courtesy Lockheed Aerospace Ceramics Systems, Sunnyvale, CA.) 11

SUMMARY • A material responds to heat by: • Heat capacity: --increased vibrational energy --redistribution of this energy to achieve thermal equil. • Heat capacity: --energy required to increase a unit mass by a unit T. --polymers have the largest values. • Coefficient of thermal expansion: --the stress-free strain induced by heating by a unit T. • Thermal conductivity: --the ability of a material to transfer heat. --metals have the largest values. • Thermal shock resistance: --the ability of a material to be rapidly cooled and not crack. Maximize sfk/Ea. 12

ANNOUNCEMENTS Reading: Chapter 17 (pdf sent to you by e-mail)