MATHEMATICAL AND NUMERICAL ANALYSIS OF THE RELATIONSHIP AMONG THE LOSCHMIDT CONSTANT, THE AVOGADRO CONSTANT, AND THE SPEED OF SOUND IN REAL GASES AT DIFFERENT THE pvT THERMODYNAMIC PROPERTIES
In this paper, a differential equation is derived that gives the relationship among the Loschmidt constant, the Avogadro constant, and the speed of sound in real gases as a function of the thermodynamic properties of the gas (pressure, temperature, and volume). The constant ratios NL/NA and the relative deviation of the NL/NA ratio from the mean value for the gases (hydrogen, helium, carbon monoxide, argon, nitrogen, oxygen, carbon dioxide, and methane) were calculated using their real-equations of state, confirming the validity of the derived equation. The first calculation of the ratio of the constants NL/NA and the relative deviation of the NL/NA ratio from the mean value for the gases at standard state (temperature 273.15 K and pressure 101,325 Pa) shows a good agreement with the published results in the literature, given the fact that the literature data of the NL/NA ratio is 0.04461498 at standard state. The second calculation of the constant ratios NL/NA and the relative deviation of the NL/NA ratio from the mean (average) value for the real gases was made for a pressure of 500,000 Pa and a temperature of 293.15 K, which also resulted in similar behavior as in previous case. The third calculation of the constant ratios NL/NA and the relative deviation of the NL/NA ratio from the mean (average) value for the real gases was made for a pressure of 1000,000 Pa and a temperature of 320.0 K, which also gave similar behavior as in previous case.
Amadeo A. Essai d’une maniere de determiner les masses relalives des molecules elementaires des corps et les proportiomes selon lesquelles elles entrent dans ces combinaisons. Vol. 73, Journal de Physique. 1811. p. 58-76,.
2.
Perrin BJ. Mouvement brownien et realite moleculaire, Annales de Chimie et de. 1909.
3.
Vol. 18, Physique,Serie. p. 1-114,.
4.
N.I.S.T. Introduction to physical constants.
5.
International Bureau of Weights and Measures. 2006.
6.
In: 14th General Conference of Weights and Measures (CGPM. 1971.
Cerovac B, Kovačević Đ. Ultrazvuk i njegova primena u tehnici I medicini. 1952.
9.
Sychev VV. The differential equations of thermodynamics. 1983.
10.
Wark K, Richards DE.
11.
Požar H. Osnove energetike (prvi svezak. 1976.
12.
Neimarlija N, Bijedić M, Imamović N. Mathematical and Numerical Analysis of the Relationship Between the Loschmidt Constant, the Avogadro Constant, and the Speed of Sound in Ideal and Real Gases at Standard State, Mašinstvo. Vol. Number 1-4, Volume 19, Journal of Mechanical Engineering. 2022. p. 37-46,.
13.
Leachman JW, Jacobsen RT, Penoncello SG, Lemmon EW. Fundamental Equations of State for.
14.
Parahydrogen NH, Ortohydrogen. Vol. 38, J. Phys. Chem. Ref. Data. 2009. p. 721-748,.
15.
Ortiz-Vega DO, Hall KR, Holste JC, Arp VD, Harvey AH, Lemmon EW. Helmholtz Equation of State for Helium, J.Phys. Chem. Ref. Data. 2020.
16.
Lemmon EW, Span R. Short Fundamental Equations of State for 20 Industrial Fluids. Vol. 51, Journal of Chemical and Engineering Data. 2006. p. 785-850,.
17.
Tegeler C, Span R, Wagner W. A New Equation of State for Agon Covering the Fluid Region for Temperatures from the Melting line to 700 K at Pressures up to 1000 MPa. Vol. 28, Journal of Physical and Chemical Reference Data. 1999. p. 779-850,.
18.
Span R, Lemmon EW, Jacobsen RT, Wagner W, Yokozeki A. A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa. Vol. 29, Journal of Physical and Chemical Reference Data. 2000. p. 1361-1433,.
19.
Schmidt R, Wagner W. A New Form of the Equation of State for Pure Substances and its Application to Oxygen. Vol. 19, Fluid Phase Equilibria. 1985. p. 175-200,.
20.
Span R, Wagner W. A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa. Vol. 25, Journal of Physical and Chemical Reference Data. 1996. p. 1509-1596,.
21.
Setzmann U, Wagner W. A New Equation of State and Tables of Thermodynamic Properties for Methane for Carbon Dioxide Covering the Range from the Melting Line to 625 K at Pressures up to 1000.
22.
MPa. Vol. 20, Journal of Physical and Chemical Reference Data. 1991. p. 1061-1151,.
Citation
Copyright
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The statements, opinions and data contained in the journal are solely those of the individual authors and contributors and not of the publisher and the editor(s). We stay neutral with regard to jurisdictional claims in published maps and institutional affiliations.
