Introduction to Materials Science and Engineering Chapter 11: Thermal Properties Textbook Chapter 20

Content Introduction Heat Capacity Thermal Expansion Thermal Conductivity 5. Thermal Stress

Introduction 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?

Introduction: In the mid-1800s, Mayer, Helmholtz, and Joule discovered independently that heat is simply a form of energy. 1853: Wiedemann and Franz law (good electrical conductors are generally good thermal conductors) The ratio between heat conductivity and electrical conductivity (divided by the temperature) is essentially constant for all metals The thermal conductivity only varies within four orders of magnitude while the electrical property varies about 25 orders of magnitude. (Fig. 18.1) – phonons, or lattice vibration quanta (Einstein)

Heat in physics is defined as energy transferred by thermal interactions. Heat flows spontaneously from systems of higher temperature to systems of lower temperature. When two systems come into thermal contact, they exchange energy through the microscopic interactions of their particles. When the systems are at different temperatures, this entails spontaneous net flow of energy from the hotter to the cooler, so that the hotter decreases in temperature and the cooler increases in temperature. This will continue until their temperatures are equal. Then the net flow of energy has settled to zero, and the systems are said to be in a relation of thermal equilibrium. Spontaneous heat transfer is an irreversible process. The first law of thermodynamics states that the internal energy of an isolated system is conserved. To change the internal energy of a system, energy must be transferred to or from the system. For a closed system, heat and work are the mechanisms by which energy can be transferred. For an open system, internal energy can be changed also by transfer of matter.[6] Work performed by a body is, by definition, an energy transfer from the body that is due to a change to external or mechanical parameters of the body, such as the volume, magnetization, and location of center of mass in a gravitational field.[2][7][8][9][10][11] When a body is heated, its internal energy increases. This additional energy is stored as kinetic and potential energy of the atoms and molecules in the body. [12] Heat itself is not stored within a body. Like work, it exists only as energy in transit from one body to another or between a body and its surroundings. (from wikipedia)

Heat, Work, And Energy First law of thermodynamics In this chapter, We limit our consideration to processes for which W can be considered to be Zero. Energy, work, and heat have same unit. 1 cal = 4.184 J 1 J = 0.239 cal

Content Introduction Heat Capacity Thermal Expansion Thermal Conductivity 5. Thermal Stress

Heat Capacity C' Heat capacity : the amount of heat which needs to be transferred to a substance in order to raise its temperature by a certain temperature interval. Generally, it is interested in two kinds : at constant volume & at constant pressure Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure. at constant V at constant P H=E+PV These relationship is….

Specific Heat Capacity, c Specific heat capacity is the heat capacity per unit mass Molar Heat Capacity, cv Molar heat capacity is the heat capacity per mole

Heated materials have the thermal energy 참고자료 Heated materials have the thermal energy How is the thermal energy stored? In the case of a water molecule http://www.2ndlaw.com/entropy.html

Solid : constrained vibration 참고자료 Monatomic gas: translation Diatomic gas : translation, rotation, vibration Liquid : translation, rotation, vibration Solid : constrained vibration vibration frequency  1012/sec → Energy Storing Mechanism

Heat Capacity vs T • Heat capacity... Cv T (K) • Atomic view: -- increases with temperature -- reaches a limiting value of 3R Adapted from Fig. 19.2, Callister 7e. gas constant 3R = 8.31 J/mol-K Cv = constant Debye temperature (usually less than T room ) T (K) q D Cv • Atomic view: -- Energy is stored as atomic vibrations. -- As T goes up, so does the avg. energy of atomic vibration

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Energy Storage How is the energy stored? Phonons – thermal waves - vibrational modes

Energy Storage Other small contributions to energy storage Electron energy levels Dominate for ceramics & plastics Energy storage in vibrational modes As energy increases the atoms vibrate faster & increase the bond distance

Specific Heat of Tungsten How much heat must be supplied to 250 g of tungsten to raise its temperature from 25oC to 650oC? If no losses occur, 5000 cal (or 20,920 J) must be supplied to the tungsten.

Specific Heat of Niobium Suppose the temperature of 50 g of niobium increases 75oC when heated for a period. Estimate the specific heat and determine the heat in calories required. How can you make a rough estimation of specific heat? → Dulong Petit’s law : Cv = 3R ≈ 6 cal/mole oC ≈ 25 J/mole oC The atomic weight of niobium is 92.91 g/mol. Thus the total heat required is:

Heat Capacity: Comparison • Why is cp significantly larger for polymers? • Polymers Polypropylene Polyethylene Polystyrene Teflon c p (J/kg-K) at room T • Ceramics M agnesia (MgO) Alumina (Al 2 O 3 ) Glass • Metals Aluminum Steel Tungsten Gold 1925 1850 1170 1050 900 486 138 128 : C : (J/mol-K) material 940 775 840 increasing c p

Content Introduction Heat Capacity Thermal Expansion Thermal Conductivity 5. Thermal Stress

Thermal Expansion • Materials change size when heating. init final L coefficient of thermal expansion (1/K or 1/°C) • Atomic view: Mean bond length increases with T. Bond energy Bond length (r) increasing T T 1 r(T5) r(T1) 5 bond energy vs bond length curve is “asymmetric”

Correlation between Bonding Strength and Materials Properties Melting Point Elastic Modulus Thermal-Expansion Coefficient

Properties from Bonding: a Thermal expansion  asymmetric nature of the energy well Broad well (generally more asymmetric)  larger expansion

Thermal Expansion: Example Ex: A copper wire 15 m long is cooled from 40 to -9°C. How much change in length will it experience? Answer: For Cu m 012 . )) C 9 ( 40 ) 15 )]( / 1 10 x 5 16 [ 6 = ° - D a l T o

Content Introduction Heat Capacity Thermal Expansion Thermal Conductivity 5. Thermal Stress

Thermal Conductivity • General: The ability of a material to transfer heat. • Quantitative: temperature gradient thermal conductivity (J/m-K-s) heat flux (J/m2-s) Fourier’s Law T 2 > T 1 x heat flux Electrons transfer from hotter region to cooler regions carry energy. Atomic vibrations in hotter region carry energy (vibrations) to cooler regions. (Lorentz number) Wiedemann and Frantz law

Thermal Conductivity: Comparison k (W/m-K) Energy Transfer Material increasing k • Metals Aluminum 247 Steel 52 Tungsten 178 Gold 315 By vibration of atoms and motion of electrons • Ceramics Magnesia (MgO) 38 Alumina (Al2O3) 39 Soda-lime glass 1.7 Silica (cryst. SiO2) 1.4 By vibration of atoms • Polymers Polypropylene 0.12 Polyethylene 0.46-0.50 Polystyrene 0.13 Teflon 0.25 By vibration/ rotation of chain molecules

Which has the lowest thermal conductivity? → vacuum Porosity in ceramic materials may have a dramatic influence on thermal conductivity; increasing the pore volume will, under most circumstances, result in a reduction of the thermal conductivity. Insulating properties of polymers are good but may be further enhanced by the introduction of small pores, which are ordinarily introduced by foaming during polymerization. → foamed polystyrene → Styrofoam

Content Introduction Heat Capacity Thermal Expansion Thermal Conductivity 5. Thermal Stress

Thermal Stress Due to restrained thermal expansion and contraction

Thermal Stress Due to temperature gradient

Thermal Stress • Occurs due to: • Example Problem 19.1, Callister 7e. -- uneven heating/cooling -- mismatch in thermal expansion. • Example Problem 19.1, Callister 7e. -- A brass rod is stress-free at room temperature (20°C). -- It is heated up, but prevented from lengthening. -- At what T does the stress reach -172 MPa?

Thermal Shock Resistance • Occurs due to: uneven heating/cooling. • Ex: Assume top thin layer is rapidly cooled from T1 to T2: s rapid quench resists contraction tries to contract during cooling T2 T1 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.

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 sf k/Ea.