Bi-Linear Model of Correlation between Heat Capacity and Volume Thermal Expansivity of Solids as a Novel Tool for Evaluation the Reliable Numerical Data for Purposes of Chemical Thermodynamics: Application to Rare Gas Solids

Vladimir Yu. Bodryakov
Head of the Department of Higher Mathematics, Ural State Pedagogical University, Yekaterinburg, Russia

Series: Physics Research and Technology
BISAC: SCI065000



Volume 10

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Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick


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A systematic study has been undertaken of basic thermodynamic functions of Rare Gas Solids (RGS) through the whole range of their solid states. These functions included isobaric molar heat capacity CP(T), volume coefficient of thermal expansion ¦Â(T), molar volume V(T), differential Gr¨¹neisen parameter ¦Ã¡ä(T), et al.
In the first section of the chapter, thermodynamic grounds are considered for hypothesizing bi-linear correlation ¦Â(CP) between heat capacities and volume thermal expansivities of non-metal solids up to the melting points (B-model). Theoretical consideration is made within unharmonic Debye-Gr¨¹neisen model without and with an account of the influence of Frenkel defects in the premelting range. Mathematical relations for the B-model are also formulated. An algorithm of applications for the B-model for least the mean squares computer analysis of scattered experimental data (CP(T), ¦Â(T), and ¦Â(CP)) of different authors are described in detail.
In the second section of the chapter, computer thermodynamic model calculations have been done within the unharmonic Debye model without and with an account of the influence of Frenkel defects in the premelting range. The validity of the B-model was verified with respect to the results of model calculations. Within the framework of the model, the influence of variation of the model parameters is estimated.
In the third section of the chapter, an evaluation of thermodynamic functions of RGS Ne, Ar, Kr and Xe up to the melting points Tm with the use of the B-model was fulfilled as an example. The choice of RGS as model objects is due to the fact that they have quite representative thermodynamic data, they do not undergo polymorphous transformations in the solid state, they have no conductivity electrons, and the effects of anharmonicity and premelting cases are most evident in RGS.
A detailed critical analysis has been carried out of the available primary sources of various data on thermodynamic properties of RGS.


Chapter 1. Thermodynamic Grounds for Hypothesizing Bi-Linear Correlation between Heat Capacities and Volume Thermal Expansivities of Solids up to the Melting Points (B-Model)

Chapter 2. Computer Thermodynamic Modelling. Properties of the B-Model

Chapter 3. Evaluation of Thermodynamic Functions of Solids with the Use of B-Model for Validation (On the Example of Rare Gas Solids)


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