Metal Debye characteristic temperatures

In this equation v is a phonon frequency, such that hv is approximately k, with the Debye characteristic temperature of the metal. The quantity p is the product of the density of electrons in energy at the Fermi surface, N(0), and the electron-phonon interaction energy, V. 

The Debye characteristic temperature of silver is 212. Calculate the atomic heat capacity Cv of this metal at 20.0° K and 300° K. 

James [G.7, p. 221] gives the following values of the characteristic Debye temperature 0 for some cubic metals. 

Here x is the distance from a reference plane, corresponding to the distance of closest approach of hydrated ions z. and C are the charge number and unperturbed concentration of the i" ionic species is the local electric potential and R, F, and T are the gas constant, Faraday s constant, and the absolute temperature. The situation is quite analogous to the junction between a semiconductor and a metal, except that, in an electrolyte, the density of ionic states close to the interface is large compared with the electronic density of states, and therefore an ionic rather than an electronic space charge forms. This perturbation in concentration extends into the electrolyte for a characteristic distance known as the Debye length ... 

Water is the most widely used dispersion liquid in inorganic chemistry because of its exceptional ability to dissolve mineral salts. It is safe, chemically stable and remains liquid over a wide temperature range. It is the solvent of choice for metallic cations because it is the most convenient reaction medium, in the laboratory as well as on an industrial scale. The ability of water to dissolve ionic and ionocovalent solids stems from two main characteristics the high polarity of the water molecule ifi = 1.84 debye) and the high dielectric constant of the liquid (e = 78.5 at 25 C). 

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