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Unformatted text preview: 1 MSE 2090: Introduction to Materials Science Chapter 19, Thermal Properties Thermal properties Â¾ Heat capacity Â¡ atomic vibrations, phonons Â¡ temperature dependence Â¡ contribution of electrons Â¾ Thermal expansion Â¡ connection to anharmonicity of interatomic potential Â¡ linear and volume coefficients of thermal expansion Â¾ Thermal conductivity Â¡ heat transport by phonons and electrons Â¾ Thermal stresses 2 MSE 2090: Introduction to Materials Science Chapter 19, Thermal Properties Heat capacity The heat capacity , C , of a system is the ratio of the heat added to the system, or withdrawn from the system, to the resultant change in the temperature: C = Ç» Q/ ' T = dQ/dT [J/deg] Â¾ This definition is only valid in the absence of phase transitions Â¾ Usually C is given as specific heat capacity , c , per gram or per mol Â¾ Heat capacity can be measured under conditions of constant temperature or constant volume. Thus, two distinct heat capacities can be defined: V V dT q C Â¸ Â¹ Â· Â¨ Â© Â§ G P P dT q C Â¸ Â¹ Â· Â¨ Â© Â§ G heat capacity at constant volume heat capacity at constant pressure C P is always greater than C V Why? Hint: The difference between C P and C v is very small for solids and liquids, but large for gases. 3 MSE 2090: Introduction to Materials Science Chapter 19, Thermal Properties Heat capacity Heat capacity is a measure of the ability of the material to absorb thermal energy. Thermal energy = kinetic energy of atomic motions + potential energy of distortion of interatomic bonds. The higher is T, the large is the mean atomic velocity and the amplitude of atomic vibrations Ã† larger thermal energy Vibrations of individual atoms in solids are not independent from each other. The coupling of atomic vibrations of adjacent atoms results in waves of atomic displacements. Each wave is characterized by its wavelength and frequency. For a wave of a given frequency Èž , there is the smallest Â¡quantumÂ¢ of vibrational energy, h Èž , called phonon . Thus, the thermal energy is the energy of all phonons (or all vibrational waves) present in the crystal at a given temperature. Scattering of electrons on phonons is one of the mechanisms responsible for electrical resistivity (Chapter 18) 4 MSE 2090: Introduction to Materials Science Chapter 19, Thermal Properties Temperature dependence of heat capacity Heat capacity has a weak temperature dependence at high temperatures (above Debye temperature È™ D ) but decreases down to zero as T approaches 0K. The constant value of the heat capacity of many simple solids is sometimes called Dulong Â¡ Petit law In 1819 Dulong and Petit found experimentally that for many solids at room temperature, c v  3R = 25 JK1 mol1 This is consistent with equipartition theorem of classical mechanics : energy added to solids takes the form of atomic vibrations and both kinetic and potential energy is associated with the three degrees of freedom of each atom....
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This note was uploaded on 03/05/2012 for the course MSE 209 taught by Professor Kelly during the Spring '08 term at UVA.
 Spring '08
 Kelly

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