TABLE 19.1 Specific Heats of Some Substances at 25°C and Atmospheric Pressure Specific Heat (J/kg - °C) Specific Heat (J/kg • °C) Substance Substance Elemental solids Other solids Aluminum 900 Brass 380 Beryllium 1 830 Glass 837 2 090 860 Cadmium 230 Ice (-5°C) Marble Copper 387 Germanium 322 Wood 1 700 Gold 129 Liquids Alcohol (ethyl) Mercury Water (15°C) Iron 448 2 400 Lead 128 703 140 Silicon 4 186 Silver 234 Gas Steam (100°C) 2 010 Note: To convert values to units of cal/g °C, divide by 4 186.
In a sample of a solid metal, each atom is free to vibrate about some equilibrium position. The atom’s energy consists of kinetic energy for motion in the x, y, and z directions plus elastic potential energy associated with the Hooke’s law forces exerted by neighboring atoms on it in the x, y, and z directions. According to the theorem of equipartition of energy, assume the average energy of each atom is 1/2 kBT for each degree of freedom. (a) Prove that the molar specific heat of the solid is 3R. The Dulong–Petit law states that this result generally describes pure solids at sufficiently high temperatures. (You may ignore the difference between the
specific heat at constant pressure and the specific heat at constant volume.) (b) Evaluate the specific heat c of iron. Explain how it compares with the value listed as shown. (c) Repeat the evaluation and comparison for gold.
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