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Similarity examination of truncated virial equation of state correspondence to linear isothermal regularity (LIR) by applying square-well (SW) potential

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Abstract

Linear isotherm regularity works very well for fluids at high densities, and it has been shown that it is compatible with the EOSs based on statistical–mechanical theory. On the other hand, at low densities, the first few terms of virial EOS have the most contribution to express the deviations from ideal behavior. For finding similarities between dense and dilute states, experimental p–v–T data of 14 fluids (He, Ne, Ar, Kr, H2, O2, N2, CO, NH3, CH3OH, CH4, C2H4, C2H6 and C3H8) are examined. Comparing the thermal dependencies of the attraction and repulsion terms (A and B) of the LIR with the second and third virial coefficients (B 2 and B 3) in liquid and supercritical regions (0.7 < T r < 3.0) shows a remarkable similarity. Square-well potential is applied to examination and comparison of theoretical results with experimental results. It is shown that in liquid and supercritical regions, (1) the short-range potential governs among particles in dense fluids, and the long-range interactions become important in the less dense fluid, (2) similar to Boyle temperature, T B, in dilute state, there is a temperature as T′B (in dense fluids) that the attractive forces and the repulsive forces acting on the dense-fluid particles balance out; thus, probably there is a maximum σ (molecular diameter) at nearly 2T c (T′B), and (3) in the liquid and supercritical regions (0.7 < T r < 3.0), in the first-order approximation, there are no significant interactions higher than triple interactions in dense-fluid particles.

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Abbreviations

LIR:

Linear isotherm regularity

LJ:

Lennard–Jones potential

SW:

Square-well potential

EOS:

Equation of state

A, B :

The thermal dependent parameters in Eq. (1)

B 2 , B 3 :

The second and third virial coefficients

b :

Co-volume

k B :

Boltzmann constant

k 1 and k 2 :

Proportionality coefficients

p :

Pressure

T :

Temperature

v :

Volume

Z :

Compression factor

σ, ε :

The parameters of the average effective LJ and SW

λ :

The parameters of SW

β :

(k B T)−1

ρ :

Molar density

B:

Boyle

c:

Critical

int:

Internal

r:

Reduced

References

  1. G.A. Parsafar, J. Sci. I. R. Iran 2, 111 (1991)

    CAS  Google Scholar 

  2. G.A. Parsafar, E.A. Mason, J. Phys. Chem. 97, 9048 (1993)

    Article  CAS  Google Scholar 

  3. B. Najafi, G.A. Parsafar, S. Alavi, J. Phys. Chem. 99, 9248 (1995)

    Article  CAS  Google Scholar 

  4. S. Alavi, G.A. Parsafar, B. Najafi, Int. J. Thermophys. 16, 1421 (1995)

    Article  CAS  Google Scholar 

  5. G.A. Parsafar, Z. Kalantar, Fluid Phase Equilib. 234, 11–21 (2005)

    Article  CAS  Google Scholar 

  6. M. Shokouhi, G.A. Parsafar, M. Dinpajooh, Fluid Phase Equilib. 271, 94–102 (2008)

    Article  CAS  Google Scholar 

  7. G.A. Parsafar, E.A. Mason, J. Phys. Chem. 98, 1962 (1994)

    Article  CAS  Google Scholar 

  8. V. Moeini, F. Ashrafi, M. Karri, H. Rahimi, J. Phys.: Condens. Matter 20, 075102 (2008)

    Google Scholar 

  9. M.M. Alavianmehr, S.M. Hosseini, B. Haghighi, J. Moghadasi, Chem. Eng. Sci. 122, 622–629 (2015)

    Article  CAS  Google Scholar 

  10. D.A. McQuarrie, Statistical Mechanics (University Science Books, Mill Valley, 2000)

    Google Scholar 

  11. Y. Song, E.A. Mason, J. Chem. Phys. 91, 12 (1989)

    Google Scholar 

  12. M. Shokouhi, G.A. Parsafar, Fluid Phase Equilib. 264, 1–11 (2008)

    Article  CAS  Google Scholar 

  13. G. Parsafar, F. Kermanpour, B. Najafi, J. Phys. Chem. B, 103, 7287–7292 (1999)

    Article  CAS  Google Scholar 

  14. J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954)

    Google Scholar 

  15. E.A. Mason, T.H. Spurling, The Virial equation of state, vol. 2 (Pergamon Press Ltd., London, 1969)

    Google Scholar 

  16. T. Kihara, Rev. Mod. Phy. 25, 831 (1953)

    Article  CAS  Google Scholar 

  17. National Institute of Standards and Technology; http://webbook.nist.gov; http://webbook.nist.gov/chemistry/fluid/

  18. Ch. Tegeler, R. Span, W. Wagner, J. Phys. Chem. Ref. Data 28, 779–850 (1999)

    Article  CAS  Google Scholar 

  19. R.B. Stewart, R.T. Jacobsen, J. Phys. Chem. Ref. Data 18, 639–798 (1989)

    Article  CAS  Google Scholar 

  20. B.A. Younglove, J. Phys. Chem. Ref. Data 11, 1–11 (1982)

    Article  Google Scholar 

  21. R.D. McCarty, V.D. Arp, Adv. Cryo. Eng. 35, 1465–1475 (1990)

    CAS  Google Scholar 

  22. R.S. Katti, R.T. Jacobsen, R.B. Stewart, Adv. Cryo. Eng. 31, 1189–1197 (1986)

    CAS  Google Scholar 

  23. A. Polt, B. Platzer, G. Maurer, Chem. Tech. (Leipzig) 44, 216–224 (1992)

    CAS  Google Scholar 

  24. J. Juza, O. Sifner, Acta Tech. CSAV. 1, 1–32 (1976)

    Google Scholar 

  25. J.W. Leachman, R.T. Jacobsen, S.G. Penoncello, E.W. Lemmon, J. Phys. Chem. Ref. Data 38, 721–748 (2009)

    Article  CAS  Google Scholar 

  26. R.D. McCarty, J. Hord, H.M. Roder, NBS Monograph 168 (National Bureau of Standards, Boulder, 1981)

    Google Scholar 

  27. R. Span, E.W. Lemmon, R.T. Jacobsen, W. Wagner, J. Phys. Chem. Ref. Data 29, 1361–1433 (2000)

    Article  CAS  Google Scholar 

  28. R.T. Jacobsen, R.B. Stewart, J. Phys. Chem. Ref. Data 15, 735–909 (1986)

    Article  CAS  Google Scholar 

  29. H. Miyamoto, K. Watanabe, Int. J. Thermophys. 21, 1045–1072 (2000)

    Article  CAS  Google Scholar 

  30. B.A. Younglove, J.F. Ely, J. Phys. Chem. Ref. Data 16, 577–798 (1987)

    Article  CAS  Google Scholar 

  31. M. Jaeschke, P. Schley, Int. J. Thermophys. 16, 1381–1392 (1995)

    Article  CAS  Google Scholar 

  32. U. Setzmann, W. Wagner, J. Phys. Chem. Ref. Data 20, 1061–1151 (1991)

    Article  CAS  Google Scholar 

  33. R.D. McCarty, National Institute of Standards and Technology (CO, Boulder, 1989)

    Google Scholar 

  34. G.A. Olchowy, J.V. Sengers, Int. J. Thermophys. 10, 417–426 (1989)

    Article  CAS  Google Scholar 

  35. R. Schmidt, W. Wagner, Fluid Phase Equilib. 19, 175–200 (1985)

    Article  CAS  Google Scholar 

  36. D.G. Friend, H. Ingham, J.F. Ely, J. Phys. Chem. Ref. Data 20, 275–347 (1991)

    Article  CAS  Google Scholar 

  37. M. Jaeschke, P. Schley, Int. J. Thermophys. 16, 1381–1392 (1995)

    Article  CAS  Google Scholar 

  38. R. Tillner-Roth, F. Harms-Watzenberg, H.D. Baehr, DKV-Tagungsbericht 20, 167–181 (1993)

    Google Scholar 

  39. J. Ahrendts, H.D. Baehr, VDI-Forsch. 596(1979)

  40. K.M. de Reuck, R.J.B. Craven, Methanol, International Thermodynamic Tables of the Fluid State—12 (IUPAC, Blackwell Scientific Publications, London, 1993)

    Google Scholar 

  41. A. Polt, B. Platzer, Chem. Tech. (Leipzig) 44, 216–224 (1992)

    CAS  Google Scholar 

  42. R.D. McCarty, Correlations for the Thermophysical Properties of Carbon Monoxide (National Institute of Standards and Technology, Boulder, 1989)

    Google Scholar 

Download references

Acknowledgement

The authors thank the Payame Noor University for financial support.

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Authors and Affiliations

  1. Department of Chemistry, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

    A. Ghandili & V. Moeini

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  1. A. Ghandili
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  2. V. Moeini
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Correspondence to V. Moeini.

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Ghandili, A., Moeini, V. Similarity examination of truncated virial equation of state correspondence to linear isothermal regularity (LIR) by applying square-well (SW) potential. J IRAN CHEM SOC 14, 883–896 (2017). https://doi.org/10.1007/s13738-016-1034-4

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