A Peer - Reviewed Journal by Nuclear Science & Technology Research Institute

Document Type : Research Paper

Authors

1 Nuclear Fuel Cycle Research School, Nuclear Science and Technology Research Institute, AEOI, P.O.Box: 11365-8486, Tehran-Iran

2 Department of Chemistry, Payame Noor University, P.O. Box: 4561934367, Abhar - Iran

Abstract

By replacing hydrogen with deuterium in water molecules, the energy level of molecular bonds changes which cause different physical, chemical, nuclear, and biological properties. Owing to that, the Equation of State (EOS) is an important and appropriate tool for studying the thermophysical behavior of materials and predicting them in different conditions in terms of pressure, temperature, and volume. Due to the importance of heavy water and its role in various researches, especially nuclear research and its application in medicine and industry, the present work aims to calculate the fugacity and virial coefficients of this material using the new generalized state equations and to compare the results obtained with experimental data to have an accurate evaluation of the equations used. The generalized equations in this research include the generalization of the equations based on the Redlich-Kwong equation (RK) and the Dietrici equation (D). The studies showed that generalization improves the results of the second virial coefficient below the critical temperature, which is more effective in the RK equation and leads to appropriate results according to the experimental data. However, in the case of fugacity, generalization improves the results in Equation D and further deviates the results in the RK equation. The results show that below the critical temperature, the van der Waals and Dietrici models do not offer a good prediction of the behavior of the third virial coefficient. Therefore, more other models should be used to predict their behavior quantitatively and qualitatively.

Highlights

1. J.A. Ayres, C.A. Trilling, Heavy water and organic fluids as neutron moderator and reflector materials, Nuclear Engineering and Design, 14, 363-389 (1971).

 

2. N. Lifson, G. B. Gordon, R. McClintock, Measurement of Total Carbon Dioxide Production by Mean of D2O, J. Appl. Physiol., 7, 704 (1955).

 

3. D.A. Schoeller, E. van Santen, Measurement of energy expenditure in humans by doubly labeled water method, J. Appl. Physiol., 53, 955 (1982).

 

4. Internationa Nuclear Information System (INIS), Heavy Water Reactors: Status and projected development, Technical Report Series, IAEA, 1-160 (2002).

 

5. N.G. Polikhronidi, et al, Isochoric Heat Capacity Measurements for Heavy Water Near the Critical Point, International Journal of Thermophysics, 23, 745-770 (2002).

 

6. J. M. H. Levelt Sengers, Assessment of Critical Parameter Values for H2O and D2O, J. Phys. Chem. Ref. Data 14, 193(1985).

 

7. L. A. Guildner, D. P. Johnson, F. E. Jones, Vapor pressure of water at its triple point: highly accurate value, Science, 191, 1261 (1976).

 

8. W.M. Jones, The triple point temperature of tritium oxide, J. Am. Chem. Soc. 74, 6065 (1952).

 

9. Robert L. Burwell, Physical Properties and Analysis of Heavy Water, Journal of Chemical Education, 30, 54 (1953)

 

10. C. H. Collie, J. B. Hasted, D. M. Ritson, The Dielectric Properties of Water and Heavy Water, Proceeding of the Physical Society, 60, 145 (1948).

 

11. P. G. Hill, R. D. Chris MacMillan, Saturation states of heavy water, J. Phys. Chem. Ref. Data, 9, 3 (1980).

 

12. P. G. Hill, R. D. MacMillan, V. Lee, A fundamental equation of state for heavy water, J. Phys. Chem. Ref. Data,11, 1 (1982).

 

13. J. Kestin, et al, Thermophysical properties of fluid D2O, J. Phys. Chem. Ref. Data, 13, 601 (1984).

 

14. C. A. Jeffery and P. H. Austin, An analytical equation of state, developed for water, J. Chem. Phys., 110, 484 (1999).

 

15. S. B. Kiselev, J. F. Ely, Parametric crossover model and physical limit of stability in supercooled water, J. Chem. Phys., 116, 5657 (2002).

 

16. S. Herrig, et al, A Reference Equation of State for Heavy Water, J. Phys. Chem. Ref. Data, 47, 043102 (2018).

 

17. M. Najafi, H.S. Kermanian, On the study of thermodynamic regularities of heavy water using van der Waals and Dieterici models, Journal of Nuclear Science and Technology, 87, 109-114 (2019).

 

18.  Y.S. Wei, R.J. Sadus, Equations of State for the Calculation of Fluid-Phase Equilibria, 46, 169-196 (2000).

 

19. A. Maghari, L. Hosseinzadeh-Shahri, Evaluation of the performance of cubic equations of state in predicting the regularities in dense fluids, Fluid Phase Equilibria, 206, 287–311 (2003).

 

20. J.S. Rowlinson, J. D.van der Waals, On the Continuity of the Gaseous and Liquid States, Elsevier, Amsterdam, 170 (1988).

 

21. O. Redlich, J.N.S. Kwong, On the Thermodynamics of  Solutions: An Equation of State. Fugacities of Gaseous Solutions, Chem. Rev, 233, 171 (1949).

 

22. N. F. Carnahan, K.E. Starling, Intermolecular Repulsions and the Equation of State for Fluids, AIChE J, 1184, 171 (1972). 

 

23. M. M. Abbott, Cubic Equation of State: An Interpretive Review, Equations of State in Engineering and Research, Adv. in Chemistry Ser., 182, K. C. Chao and R. L. Robinson eds., American Chemical Society, Washington, DC, (1979).

 

24. D.Y. Peng, D.B. Robinson, ‘A New Two-Constant Equation of State, Ind. Eng. Chem. Fundam, 59,  171 (1976).

 

25. G. Soave, Equilibrium Constants from a Modified Redlich-Kwong Equation of State, Chem. Eng. Sci., 27, 171 (1972).

 

26. C.  Dieterici, Ann. Phys. Chem. Wiedemanns Ann., 685, 1460 (1899).

 

27. R.J. Sadus, Equations of state for fluids: The Dieterici approach revisited, J. Chem. Phys, 115, 1460 (2001).

 

28. R. Balasubramanian, A study on the generalization of equations of state for liquid and gases, Open Journal Modern Physics, 1, 34 (2014).

 

29. L. Meng, Y-Y Duan, L. Lei, Correlations for second and third virial coefficients of pure fluids Fluid Phase Equilibria, 226, 109 (2004).

 

30. M.J.  Assael, J.P.M. Trusler, T.F. Tsolakis, An introduction to their Prediction Thermophysical Properties of Fluids, Imperial College Press, London, UK, (1996).

 

31. G.S. Kell, G.E. McLaurin, E. Whalley, PVT Properties of Water. Virial Coefficients of D2O in the Range 150°–500°C, J. Chem. Phys., 49, 2839 (1968).

 

32. G. Garberoglio, et al, Fully quantum calculation of the second and third virial coefficients of water and its isotopologues from ab initio potentials, Faraday Discussions, 212, 467 (2018).

 

33. NIST Chemistry WebBook, www.nist.gov.

Keywords

1. J.A. Ayres, C.A. Trilling, Heavy water and organic fluids as neutron moderator and reflector materials, Nuclear Engineering and Design, 14, 363-389 (1971).
 
2. N. Lifson, G. B. Gordon, R. McClintock, Measurement of Total Carbon Dioxide Production by Mean of D2O, J. Appl. Physiol., 7, 704 (1955).
 
3. D.A. Schoeller, E. van Santen, Measurement of energy expenditure in humans by doubly labeled water method, J. Appl. Physiol., 53, 955 (1982).
 
4. Internationa Nuclear Information System (INIS), Heavy Water Reactors: Status and projected development, Technical Report Series, IAEA, 1-160 (2002).
 
5. N.G. Polikhronidi, et al, Isochoric Heat Capacity Measurements for Heavy Water Near the Critical Point, International Journal of Thermophysics, 23, 745-770 (2002).
 
6. J. M. H. Levelt Sengers, Assessment of Critical Parameter Values for H2O and D2O, J. Phys. Chem. Ref. Data 14, 193(1985).
 
7. L. A. Guildner, D. P. Johnson, F. E. Jones, Vapor pressure of water at its triple point: highly accurate value, Science, 191, 1261 (1976).
 
8. W.M. Jones, The triple point temperature of tritium oxide, J. Am. Chem. Soc. 74, 6065 (1952).
 
9. Robert L. Burwell, Physical Properties and Analysis of Heavy Water, Journal of Chemical Education, 30, 54 (1953)
 
10. C. H. Collie, J. B. Hasted, D. M. Ritson, The Dielectric Properties of Water and Heavy Water, Proceeding of the Physical Society, 60, 145 (1948).
 
11. P. G. Hill, R. D. Chris MacMillan, Saturation states of heavy water, J. Phys. Chem. Ref. Data, 9, 3 (1980).
 
12. P. G. Hill, R. D. MacMillan, V. Lee, A fundamental equation of state for heavy water, J. Phys. Chem. Ref. Data,11, 1 (1982).
 
13. J. Kestin, et al, Thermophysical properties of fluid D2O, J. Phys. Chem. Ref. Data, 13, 601 (1984).
 
14. C. A. Jeffery and P. H. Austin, An analytical equation of state, developed for water, J. Chem. Phys., 110, 484 (1999).
 
15. S. B. Kiselev, J. F. Ely, Parametric crossover model and physical limit of stability in supercooled water, J. Chem. Phys., 116, 5657 (2002).
 
16. S. Herrig, et al, A Reference Equation of State for Heavy Water, J. Phys. Chem. Ref. Data, 47, 043102 (2018).
 
17. M. Najafi, H.S. Kermanian, On the study of thermodynamic regularities of heavy water using van der Waals and Dieterici models, Journal of Nuclear Science and Technology, 87, 109-114 (2019).
 
18.  Y.S. Wei, R.J. Sadus, Equations of State for the Calculation of Fluid-Phase Equilibria, 46, 169-196 (2000).
 
19. A. Maghari, L. Hosseinzadeh-Shahri, Evaluation of the performance of cubic equations of state in predicting the regularities in dense fluids, Fluid Phase Equilibria, 206, 287–311 (2003).
 
20. J.S. Rowlinson, J. D.van der Waals, On the Continuity of the Gaseous and Liquid States, Elsevier, Amsterdam, 170 (1988).
 
21. O. Redlich, J.N.S. Kwong, On the Thermodynamics of  Solutions: An Equation of State. Fugacities of Gaseous Solutions, Chem. Rev, 233, 171 (1949).
 
22. N. F. Carnahan, K.E. Starling, Intermolecular Repulsions and the Equation of State for Fluids, AIChE J, 1184, 171 (1972). 
 
23. M. M. Abbott, Cubic Equation of State: An Interpretive Review, Equations of State in Engineering and Research, Adv. in Chemistry Ser., 182, K. C. Chao and R. L. Robinson eds., American Chemical Society, Washington, DC, (1979).
 
24. D.Y. Peng, D.B. Robinson, ‘A New Two-Constant Equation of State, Ind. Eng. Chem. Fundam, 59,  171 (1976).
 
25. G. Soave, Equilibrium Constants from a Modified Redlich-Kwong Equation of State, Chem. Eng. Sci., 27, 171 (1972).
 
26. C.  Dieterici, Ann. Phys. Chem. Wiedemanns Ann., 685, 1460 (1899).
 
27. R.J. Sadus, Equations of state for fluids: The Dieterici approach revisited, J. Chem. Phys, 115, 1460 (2001).
 
28. R. Balasubramanian, A study on the generalization of equations of state for liquid and gases, Open Journal Modern Physics, 1, 34 (2014).
 
29. L. Meng, Y-Y Duan, L. Lei, Correlations for second and third virial coefficients of pure fluids Fluid Phase Equilibria, 226, 109 (2004).
 
30. M.J.  Assael, J.P.M. Trusler, T.F. Tsolakis, An introduction to their Prediction Thermophysical Properties of Fluids, Imperial College Press, London, UK, (1996).
 
31. G.S. Kell, G.E. McLaurin, E. Whalley, PVT Properties of Water. Virial Coefficients of D2O in the Range 150°–500°C, J. Chem. Phys., 49, 2839 (1968).
 
32. G. Garberoglio, et al, Fully quantum calculation of the second and third virial coefficients of water and its isotopologues from ab initio potentials, Faraday Discussions, 212, 467 (2018).
 
33. NIST Chemistry WebBook, www.nist.gov.