In a sample of a solid metal, each atom is free tovibrate about some equilibrium

Chapter 21, Problem 50

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In a sample of a solid metal, each atom is free tovibrate about some equilibrium position. The atomsenergy consists of kinetic energy for motion in the x, y, and z directions plus elastic potential energy associatedwith the Hookes law forces exerted by neighboringatoms on it in the x, y, and z directions. Accordingto the theorem of equipartition of energy, assume theaverage energy of each atom is 12kBT for each degree offreedom. (a) Prove that the molar specific heat of thesolid is 3R. The DulongPetit law states that this resultgenerally describes pure solids at sufficiently high temperatures.(You may ignore the difference between thespecific heat at constant pressure and the specific heatat constant volume.) (b) Evaluate the specific heat c ofiron. Explain how it compares with the value listed inTable 20.1. (c) Repeat the evaluation and comparisonfor gold.

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