Heat Capacity_Part_2

Heat Capacity_Part_2 - Heat capacity of solids Dulong Petit...

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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei Heat capacity of solids – Dulong – Petit law In 1819 Dulong and Petit found experimentally that for many solids at room temperature, c v 3R = 25 JK -1 mol -1 This is consistent with equipartition theory: 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. T k 2 3 ) t ( K ) t ( P B = = The molar internal energy is then U = 3N A kT = 3RT and the molar constant volume heat capacity is c v = [ U/ T] v =3R Although c v for many elements at room T are indeed close to 3R, low-T measurements found a strong temperature dependence of c v . Actually, c v 0 as T 0 K.
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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei Heat capacity of solids – Einstein model The low-T behavior can be explained by quantum theory. The first explanation was proposed by Einstein in 1906. He considered a solid as an ensemble of independent quantum harmonic oscillators vibrating at a frequency υ . Quantum theory gives the energy of i th level of a harmonic quantum oscillator as ε i = (i + ½) h υ where i = 0,1,2…, and h is Planck’s constant. For a quantum harmonic oscillator the Einstein-Bose statistics must be
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Heat Capacity_Part_2 - Heat capacity of solids Dulong Petit...

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