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the general expressions

The most important thermodynamic properties of molecules in a condition idealyonogo gas are intrinsic energy (U), enthalpy (H), entropy (S), free eneryogija Gibbs (G), free energy Gelmgoltsa (F) and heat capacity (CP).

In frameworks statiyosticheskoj physicists can be calculated them direct summation on energijam terms poyosredstvom the statistical sum (Q). Thus, sizes of properties (U, H, S, G, F) okazyyovajutsja in the potentials defined to within an arbitrary constant, and their numerical value depends on a choice of a datum of energy levels. Routinely as that on the power diagramme the basic electronic term, and in geometrical interpretation - a minimum on a potential energy surface (PPE) acts.

According to definition [307, 308], the statistical sum of a molecule is expressed by the formula

Where summation is carried out on all power terms - energijam the core and excited states Ei. In other representation from the statistical sum (4.9) evolve energy of the basic oscillatory condition (energy of zero fluctuations E0) in a separate multiplier. It result ins to parities (4.10) ÷ (4.15), containing eneryogii transferrings AEiс of the raised levels to the basic (energy AEiчасто register through frequencies of transferrings ωi) '.

Here T - absolute temperature [K], to - a Boltzmann's constant [Dzh/to], h - Planck's constant [J-with], ωi - frequency [sm-1], with - a velocity of light [sm/with].

In recalculation on 1 mole of molecules of one grade and taking into account their identity (isyokljuchaja a case of very low temperatures, small volumes and high densities) values of thermodynamic properties of ideal gas concerning a potential trough bottom on Ш1Э are equal:

Where R - universal (molar) gas constant [J-MOLE-1-K-1], Na - constant Avogadro [mole-1]. Representation of contributions of zero fluctuations (U0, H0, G0, F0) in properties in an explicit form corresponds to expressions (4.22) ÷ (4.27):

Expressions in the right parts (4.22) ÷ (4.27) - temperature shifts of all termodiyonamicheskih potentials U, H, G, F - are counted from the basic vibrational level of energy on the power diagramme (E0), and Qопределяется on a parity (4.15). At T = 0 To temperature shift zanuljaetsja, and sizes of potentials U, H, G, Fоказываются equal E0 then-U0, HT-H0, GT-G0, FT-F0 it is possible to redefine differences UT as:

Values of entropy and heat capacity do not depend on energy of zero fluctuations, they have no binding on the power diagramme (expressions 4.20, 4.21 and 4.26, 4.27) and, besides, heat capacity is absolute value Cp (0) = 0. ^glasno to theorem nernsta entropy of an ideal crystal at T = 0 To does not depend from thermodynamic payorametrov and in most cases also is equal to zero, i.e. S (0) = 0, however for ideal gas of not charged molecules and for lack of external fields S (0) generally not opredeyolena. Its size it is possible to present as entropy of phase change «ideal kriyostall → ideal gas» at T = 0 K.Obychno in this hypothetical size or preneyobregajut (i.e. believe S (0) = 0), or privately include it in the forward contribution and, tayokim in the image, count entropy Sв (4.20) and (4.26) from S (0).

4.4.2.

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A source: Turovtsev Vladimir Vladimirovich. Creation and application of a quantum mechanical model for calculating the thermodynamic properties of substances in a wide range of temperatures. Thesis for the degree of doctor of physico-mathematical sciences. Tver - 2014. 2014

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