Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

An Analytical Equation of State for Molten Alkaline and Alkaline Earth Metals from Critical Point Constants

Document Type : Research Paper

Authors

M.H Mousazadeh
Z Mousapoor
Abstract
Alkali metals have a unique combination of physicochemical properties, such as extremely high electrical and thermal conductivities, law densities and viscosities, wide temperature ranges of a liquid state, great heat of evaporation, etc. Therefore, they are widely used in modern science and technology, especially liquid alkali metals act as a coolant in nuclear power plants. In this work, we developed an equation of state (EoS) based on statistical–mechanical perturbation theory for alkaline and alkaline earth metals. The theoretical EoS undertaken is Ihm–Song–Mason (ISM), and there are three temperature-dependent quantities that are required to use the EoS: the second virial coefficients B2(T), an effective van der Waals covolume, b(T) and a correction factor, α(T). Those are calculated from a two-parameter corresponding states correlation, which is constructed with two constants as scaling parameters, i.e., the temperature, Tc and molar density ρc at critical points. This new correlation has been applied to the ISM EoS to predict the volumetric behavior of alkali and alkali earth metals. We have tested the predicted EoS against the experimental data. The results show that in comparison to previous works, the present correlation is more accurate and covers a much wider range of temperature and pressure.

Highlights

  1. 1.    R. D. Kale, M. Rajan, Developments in sodium technology, Curr. Sci. 86 (2004) 668-675.

 

  1. 2.    M. H. Mousazadeh, Corresponding states theory and thermodynamic properties of liquid alkali metals, J. Iranian Chem. Soc., 3 (2006) 22-31.

 

  1. 3.    M. H. Mousazadeh, A perturbed Lennard–Jones chain equation of state for liquid Metals, J. Phys.: Condensed Matter, 18 (2006) 4793-4800.

 

  1. 4.    M. H. Mousazadeh, A perturbed Lennard–Jones chain equation of state for liquid refractory metals, J. Non-Crystalline Solids, 353 (2007) 435-439.

 

  1. 5.    M. H. Mousazadeh, Equation of state for thermodynamic properties of pure and Mixtures liquid alkali metals, Thermochimica Acta, 511 (2010) 147-151.

 

  1. 6.    M. H. Mousazadeh, H. Diarmand, A perturbed Yukawa chain equation of state for liquid metals, J. of Mol. Liquids, 170 (2012) 41-44.

 

  1. 7.    Y. S. Wei, R. J. Sadus, Am. Inst. Chem. Eng. J. 46 (2000) 169-196.

 

  1. 8.    J. A. Barker, D. Henderson, J. Chem. Phys. 47 (1967) 4714-4721.

 

  1. 9.    N. F. Carnahan, K. E. Starling, J. Chem. Phys. 51 (1969) 635-636.

 

10. Y. Song, E. A. Mason, Statistical mechanical theory of a new analytical.

 

11. G. Ihm, Y. Song, E. A. Mason, A new principle of corresponding states for nonpolar fluids, J. Chem. Phys. 94 (1991) 3839-3848.

 

12. A. Boushehri, M. H. Keshavarz, The liquid density of complex liquid mixtures, Bull. Chem. Soc. Jpn. 67 (1994) 1213-1216.

 

13. M. H. Mousazadeh, A. Boushehri, Equation of state for complex liquid mixtures from surface tension, Int. J. Thermophys. 17 (1996) 945-957.

 

14. M. H. Mousazadeh, A. Boushehri, A correlation of densities of liquid natural gas mixtures from surface tension, Fluid Phase Equilib. 168 (2000) 125-134.

15. M. M. Ghatee, A. Boushehri, An analytical equation of state for molten alkali metals, Int. J. Thermophys. 16 (1995) 1429-1438.

 

16. M. M. Ghatee, A. Boushehri, Equation of state for compressed liquids from surface tension, Int. J. Thermophys. 17 (1996) 945-957.

 

17. F. M. Tao, E. A. Mason, Equation of state for mixtures of nonpolar fluids, Int J. Thermophys 13 (1992) 1053-60.

 

18. K. S. Pitzer, R. F. Curl Jr, The volumetric and thermodynamics properties of fluids, J Am Chem Soc 79 (1957) 2369-70.

 

19. A. Boushehri, E. A. Mason, Equation of state for compressed liquids and their mixtures from the cohesive energy density, Int. J. Thermophys. 14 (1993) 685-697.

 

20. H. Karimi, F. Yousefi, M. M. Papari, PVTx Properties of liquefied Natural Gas Mixtures Using Tao-Mason Equation of state, J. Chem Eng. Japan 44 (2011) 295-303.

 

21. M. M. Papari, M. Kiani, R. Behjatmanesh-Ardakani, J. Moghadasi, A. Campo, Equation of state and P–V–T properties of polymer melts based on glass transition data, Journal of Molecular Liquids 16 (2011) 148-152.

 

22. F. Yousefi, M. Kaveh, Tao-Mason equation of state for refractory metals, Indian J. Sci. & Tech. 5 (2012) 2363-68.

 

23. F. Yousefi, H. Karimi, Modification of Tao-Mason equation of state to Ionic liquids, Ionics. (2011) DOI.10.1007/s11581-011-0605-8.

 

24. C. Tsonopoulos, J. L. Heidman, From the virial to the cubic equation os state, Fluid Phase Equilib. 57 (2003) 261-276.

 

25. Y. Song, E. A. Mason, Statistical mechanical basis for accurate analytical equation of state for fluids, Fluid Phase Equilib. 75 (1992) 105-115.

 

26. N. B. Vargaftik, Handbook of Physical Properties of Liquids and Gases, Hemisphere, Washington, DC (1975).

 


Keywords

Alkaline and Alkaline Earth Metals
Critical Constants
Equation of State
Perturbation Theory
  1. 1.    R. D. Kale, M. Rajan, Developments in sodium technology, Curr. Sci. 86 (2004) 668-675.

 

  1. 2.    M. H. Mousazadeh, Corresponding states theory and thermodynamic properties of liquid alkali metals, J. Iranian Chem. Soc., 3 (2006) 22-31.

 

  1. 3.    M. H. Mousazadeh, A perturbed Lennard–Jones chain equation of state for liquid Metals, J. Phys.: Condensed Matter, 18 (2006) 4793-4800.

 

  1. 4.    M. H. Mousazadeh, A perturbed Lennard–Jones chain equation of state for liquid refractory metals, J. Non-Crystalline Solids, 353 (2007) 435-439.

 

  1. 5.    M. H. Mousazadeh, Equation of state for thermodynamic properties of pure and Mixtures liquid alkali metals, Thermochimica Acta, 511 (2010) 147-151.

 

  1. 6.    M. H. Mousazadeh, H. Diarmand, A perturbed Yukawa chain equation of state for liquid metals, J. of Mol. Liquids, 170 (2012) 41-44.

 

  1. 7.    Y. S. Wei, R. J. Sadus, Am. Inst. Chem. Eng. J. 46 (2000) 169-196.

 

  1. 8.    J. A. Barker, D. Henderson, J. Chem. Phys. 47 (1967) 4714-4721.

 

  1. 9.    N. F. Carnahan, K. E. Starling, J. Chem. Phys. 51 (1969) 635-636.

 

10. Y. Song, E. A. Mason, Statistical mechanical theory of a new analytical.

 

11. G. Ihm, Y. Song, E. A. Mason, A new principle of corresponding states for nonpolar fluids, J. Chem. Phys. 94 (1991) 3839-3848.

 

12. A. Boushehri, M. H. Keshavarz, The liquid density of complex liquid mixtures, Bull. Chem. Soc. Jpn. 67 (1994) 1213-1216.

 

13. M. H. Mousazadeh, A. Boushehri, Equation of state for complex liquid mixtures from surface tension, Int. J. Thermophys. 17 (1996) 945-957.

 

14. M. H. Mousazadeh, A. Boushehri, A correlation of densities of liquid natural gas mixtures from surface tension, Fluid Phase Equilib. 168 (2000) 125-134.

15. M. M. Ghatee, A. Boushehri, An analytical equation of state for molten alkali metals, Int. J. Thermophys. 16 (1995) 1429-1438.

 

16. M. M. Ghatee, A. Boushehri, Equation of state for compressed liquids from surface tension, Int. J. Thermophys. 17 (1996) 945-957.

 

17. F. M. Tao, E. A. Mason, Equation of state for mixtures of nonpolar fluids, Int J. Thermophys 13 (1992) 1053-60.

 

18. K. S. Pitzer, R. F. Curl Jr, The volumetric and thermodynamics properties of fluids, J Am Chem Soc 79 (1957) 2369-70.

 

19. A. Boushehri, E. A. Mason, Equation of state for compressed liquids and their mixtures from the cohesive energy density, Int. J. Thermophys. 14 (1993) 685-697.

 

20. H. Karimi, F. Yousefi, M. M. Papari, PVTx Properties of liquefied Natural Gas Mixtures Using Tao-Mason Equation of state, J. Chem Eng. Japan 44 (2011) 295-303.

 

21. M. M. Papari, M. Kiani, R. Behjatmanesh-Ardakani, J. Moghadasi, A. Campo, Equation of state and P–V–T properties of polymer melts based on glass transition data, Journal of Molecular Liquids 16 (2011) 148-152.

 

22. F. Yousefi, M. Kaveh, Tao-Mason equation of state for refractory metals, Indian J. Sci. & Tech. 5 (2012) 2363-68.

 

23. F. Yousefi, H. Karimi, Modification of Tao-Mason equation of state to Ionic liquids, Ionics. (2011) DOI.10.1007/s11581-011-0605-8.

 

24. C. Tsonopoulos, J. L. Heidman, From the virial to the cubic equation os state, Fluid Phase Equilib. 57 (2003) 261-276.

 

25. Y. Song, E. A. Mason, Statistical mechanical basis for accurate analytical equation of state for fluids, Fluid Phase Equilib. 75 (1992) 105-115.

 

26. N. B. Vargaftik, Handbook of Physical Properties of Liquids and Gases, Hemisphere, Washington, DC (1975).

 


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