New Physical and Chemical Constants and Prospects of Its Use for the Explicit Expression of Thermodynamic Functions

Based on the analysis of the Boltzmann＇s distribution in an infinitely high temperature found degeneration of the thermodynamic system in a purely informational with independently of each particle on its energy level, thus providing them full visibility of and the ability to calculate the maximum entropy in the Boltzmann formula S∞ = R·InNA = 455.251 J/（mol.K）. This value, when expressed in terms of fundamental constants, is itself a physical and chemical constants and mole monatomic ideal gas is unsurpassed in any studied temperature range. For complex substances this limit increases in direct proportion to their atomic. The existence of two limits entropy change--lower, equal to zero according to the third law of thermodynamics, and the top, equal to S∞, makes possible the explicit expression of the temperature dependence of the entropy in the form of an exponentialS=S∞exp[-5030.31p 2/5 /（M3/5T）]（5/2）r e/s∞. rather than in the form of a logarithmic dependence of the infinite by the approximateformula Sakura-Tetrode with which this the dependence is almost identical in the studied temperature range （100-10,000 K）, but not absurd negative entropy in the extrapolation formula Sakura-Tetrode absolute zero to the region and especially in the area of T → ∞where it turns S →∞.

The Concept of Randomized Particles as the Basis of Cluster and Associate Theory Viscosity and Flow

Using thermal barriers at the melting point?Hm and RTm,it is shown that the latter directly reflects the chaotic process,since it is equal to the kinetic energy reserve of chaotic(thermal)particle motions,and the first additionally takes into account the energy expenditure for overcoming the potential energy of the interconnection of particles,which is typical for inorganic compounds.Therefore,to determine the share of crystal-mobile particles responsible for the viscosity of the melt,the chaotization barrier of RTm should be used,since in the virtual clusters the potential binding energy is conserved,thereby compensating for the heat expense of breaking these bonds upon melting.Therefore,to analyze the share of crystal-mobile particles,it is necessary to use the formula of their share in the form:Pcrm=1-exp(-tm/t).On the basis of the distribution of clusters previously found by the authors in terms of the number of crystal-mobile particles included in them,it was shown that all non-single crystal-mobile particles are responsible for the viscosity,and for flowability all single particles,including crystal-mobile,liquid-mobile and vapor-mobile.This ensures the superiority of the share of single particles over the share of crystal-mobile particles arranged in non-single clusters at the melting point,and thereby the fluidity of the melt.Based on the share distribution of clusters in terms of the number of particles entering into them,the share of non-single clusters responsible for the viscosity of the melt is expressed as:Pct=p2crm=[1-exp(-Tm/T)2].The probabilistic meaning of the formation of clusters from non-single crystal-mobile particles is extended to the formation of associates,which made it possible to disclose the meaning of the second level of the exponential dependence of viscosity in the cluster and associate model:η=η1(T1/T)a2(T2/T)b,where the first level is responsible for the formation of clusters,and the second—for associates.This form corresponds to the physical hierarchy when combining crystal-mobile particles.The previously proposed method for processing viscosity data for the cluster and associate model assumed the use of three reference points from the available experimental array of values of viscosity at different temperatures.This method is supplemented by using the entire set of data on the viscosity with the preservation of two reference points and processing the rest to determine the exponent b,which has the meaning of aggregation degree of associates,from the linearized dependence:ln in(η/η1)in(T1/T2)/IN(T1/T)in(η/η1)=bin(T1/T).The new method was tested on reference data and showed its high statistical adequacy.

The Relation between the Heat of Melting Point, Boiling Point, and the Activation Energy of Self-Diffusion in Accordance with the Concept of Randomized Particles

On the example of typical metals, it’s found that the activation energy of self-diffusion is above of the melting heat and below of vaporization heat. This corresponds to the existence of liquid-mobile particle classification based on the concept of randomized particles. A formula for estimating the activation energy of self-diffusion by which it is approximately half of the heat of evaporation of the substance is recommended. We derive the temperature dependence for a fraction self-diffusion’s particles.

Quantization of Particle Energy in the Analysis of the Boltzmann Distribution and Entropy

The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commensuration coefficient of discrete and continuous similarly-named distributions developed by the authors, the article analyses the statistical sum in the Boltzmann distribution to the commensuration with the improper integral of the similarly-named function in the full range of the term of series of the statistical sum at the different combination of the temperature and the step of variation （quantum） of the particle energy. The convergence of series based on the Cauchy, Maclaurin criteria and the equal commensuration of series and improper integral of the similarly-named function in each unit interval of variation of series and similarly-named function were estab- lished. The obtained formulas for the commensuration coefficient and statistical sum were analyzed, and a general expres- sion for the total and residual statistical sums, which can be calculated with any given accuracy, is found. Given a direct calculation formula for the Boltzmann distribution, taking into account the values of the improper integral and commensuration coefficient. To determine the entropy from the new expression for the Boltzmann distribution in the form of a series, the conver- gence of the similarly-named improper integral is established. However, the commensuration coefficient of integral and series in each unit interval turns out to be dependent on the number of the term of series and therefore cannot be used to determine the sum of series through the improper integral. In this case, the entropy can be calculated with a given accuracy with a corresponding quantity of the term of series n at a fixed value of the statistical sum. The given accuracy of the statistical sum turns out to be mathematically identical to the fraction of particles with an energy exceeding a given level of the energy barrier equal to the activation energy in the Arrhenius equation. The prospect of development of the proposed method for expressing the Boltzmann distribution and entropy is to establish the relationship between the magnitude of the energy quantum Ae and the properties of the system-forming particles.

Cluster-Associate Model of Viscosity of Silver Chloridein Comparison with Frenkel Model

The purpose of the research is to develop the temperature dependence of the dynamic viscosity for silver chloride. The data were calculated on the basis of a new cluster and associate equation, which was derived using the concept of randomized particles. The calculated data are given in the temperature range from the melting point to the boiling point. The cluster and associate model is compared with the Frenkel’s equation in logarithmic coordinates, showing the mutual correspondence and complementarity of these models.

Clusters: Viscosity Cause?

The significance of the work is determined by the need to develop a cluster theory of the liquid state of a substance in order to more deeply substantiate the viscosity, which is still expressed by empirical parameters within the framework of ideal ideas about the stratified flow of a liquid. According to the reference data on the dynamic viscosity of the melts for chlorides of the first group of the Periodic System, the approximating dependences in the form of cluster-associate and Frenkel’s models were constructed at various temperatures. The first model is based on taking into account the share of particles that cannot overcome the thermal melting barrier and thus serve to form virtual clusters and associates while preserving the structural motifs of the solid phase. In the framework of the cluster-associate viscosity model developed by the authors, these formations determine the melt viscosity and serve as flow units to which the energy of fluid motion is applied. The Frenkel’s model allows us to estimate the activation energy of fluidity. Calculations show that by comparing this energy with the degree of cluster association obtained in the framework of the cluster-associate model, a fairly close linear correlation is obtained, and the proportionality coefficient has the meaning of the activation energy per cluster. This energy does not go beyond the van der Waals energy of the unsaturated intermolecular bond characteristic of the interaction of particles in a liquid. This confirms the earlier established by the authors a similar pattern for melts of simple substances, based on the understanding of fluidity as a consequence of the destruction of cluster associates while preserving the clusters themselves.