Abstract
In this paper, we propose a new approach for accurate evaluation of speed of sound and specific heat capacities of gases by using analytical formulae of the quantum mechanical and classical second virial coefficients with the Lennard-Jones (12-6) potential. Also, the first and second derivatives of the virial coefficient have been established. The efficiency of the methods is thoroughly examined by applying obtained formulae to the evaluation of some properties of molecules He, Ne, Kr, Xe, Ar, H2, D2, O2 and CH4. The results of the analytical and literature calculations in the case of arbitrary temperature are compared. The suggested method can be used to improve the correctness of quantum correction to classical second virial coefficient evaluation and their first and second derivatives. The proposed approach allows us to calculate the thermodynamic parameters using quantum second virial coefficients with more accuracy and reliability.
Similar content being viewed by others
References
C.G. Gray, K.E. Gubbins, C.G. Joslin, Theory of Molecular Fluids (Oxford University Press, Oxford, 2011)
D.A. McQuarrie, Statistical Mechanics (Harper Row, New York, 1973)
K. Lucas, Applied Statistical Thermodynamics (Springer, Berlin, 1991)
L. Gropper, Phys. Rev. 51, 1108 (1937)
W.F. Wang, J. Quant. Spectrosc. Radiat. Transf. 76, 23–30 (2003)
N. Corbin, W.J. Meath, A.R. Allnatt, Mol. Phys. 53, 225–232 (1984)
T.S. Nilsen, Phys. Rev. 186, 262–264 (1969)
J.J. D’Arruda, R.N. Hill, Phys. Rev. A 1, 1791–1802 (1970)
M. McCarty, S.V.K. Babu, J. Phys. Chem. 74, 1113–1115 (1970)
H.B. Ghassib, A.S. Sandouqa, B.R. Joudeh, S.M. Mosameh, Can. J. Phys. 92, 997–1001 (2014)
B.A. Mamedov, E. Somuncu, J. Phys. Conf. Ser. 766, 012010 (2016)
D.A. McQuarrie, J.D. Simon, Physical Chemistry: A Molecular Approach (University Science Books, Sausalito, 1997)
J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954)
I.G. Kaplan, Intermolecular Interactions: Physical Picture, Computational Methods and Model Potentials (Wiley, New York, 2006)
I.S. Gradshteyn, I.M. Ryzhik, Tables of Integrals, Series and Products (Academic Publisher, London, 1965)
E. Copuroglu, J. Chem. 2017, 1598951 (2017)
E. Copuroglu, T. Mehmetoglu, IEEE Trans. Electron Device 62, 1580–1583 (2015)
M. Abramowitz, I.A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Government Printing Office, New York, 1972)
M.E. Boyd, J. Res. Natl. Bureau Stand. Sect. A 75A, 57–95 (1971)
J. De Boer, A. Michels, Physica 10, 945–957 (1938)
S.H. Ling, M.J. Rigby, J. Phys. Chem. 86, 1469–1472 (1982)
B.A. Mamedov, E. Somuncu, J. Mol. Struct. 1068, 164–169 (2014)
CEARUN, NASA. https://cearun.grc.nasa.gov
eThermo Thermodynamics & Transport Properties Calculation. http://www.ethermo.us
Acknowledgements
This work has been supported by the Amasya University BAP (Project No: FMB-BAP 18-0330)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Somuncu, E., Oner, F., Orbay, M. et al. A comparative evaluation of speed of sound and specific heat capacities of gases by using the quantum mechanical and classical second virial coefficients. J Math Chem 57, 1935–1948 (2019). https://doi.org/10.1007/s10910-019-01049-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-019-01049-6