Characteristic temperature theorem

EOV EOS theory was developed by formulation of canonical function of the Boltzmann distribution of energies and derivation of thermodynamic pressure. The theorem of corresponding states says that the same compressibility factor can be expected for all fluids when compared at reduced temperature and pressure. A two-parameter correlation for compressibility factor, Z, can be derived using the theorem of corresponding states. EOV EOS obeys the corresponding state principle. Characteristic temperature, pressure, and specific volume used in EOV EOS are tabulated for 16 commonly used polymers. 

Planck (loc. cit. 276) has observed that the point on which the whole matter turns is the establishment of a characteristic equation for each substance, which shall agree with Nernst s theorem. For if this is known we can calculate the pressure of the saturated vapour by means of Maxwell s theorem ( 90). He further remarks that, although a very large number of characteristic equations (van der Waals, Clausius s, etc.) are in existence, none of them leads to an expression for the pressure of the saturated vapour which passes over into (9) 210, at very low temperatures. Another condition which must be satisfied is... 

Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... 

The density functional theory of Hohenberg, Kohn and Sham [173,205] has become the standard formalism for first-principles calculations of the electronic structure of extended systems. Kohn and Sham postulate a model state described by a singledeterminant wave function whose electronic density function is identical to the ground-state density of an interacting /V-clcctron system. DFT theory is based on Hohenberg-Kohn theorems, which show that the external potential function v(r) of an //-electron system is determined by its ground-state electron density. The theory can be extended to nonzero temperatures by considering a statistical electron density defined by Fermi-Dirac occupation numbers [241], The theory is also easily extended to the spin-indexed density characteristic of UHF theory and of the two-fluid model of spin-polarized metals [414],... 

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