A novel scheme for predicting the behaviors of liquid and vapor phases of water using the ideal gas theory

Abstract

     The ideal gas equation of state is the simplest equation of state for estimating the values of temperature, pressure and volume. This equation of state has a simple structure based on its simple theory. Hence, it has an explicit relation between these variables. In addition, calculating other thermodynamic properties (such as, internal energy, enthalpy and specific heats) is very simple for ideal gases. In this study, the ideal gas theory has been applicable for the liquid and vapor phases of water. To this aim, the temperature and molar volume have been modified as functions of the fluid molecular compressibility. In the presented method, effects of the temperature and volume on the non-ideality of the behaviors are considered, separately. Comparing the predicted values with the real data shows at least R-squared value equal to 0.98. 

Keywords

• Water,Ideal gas theory,Equation of state

References

1. [1]. D.Y. Peng, D.B. Robinson, A new two-constant equation of state, Ind. Eng. Chem. Fundam. 15 (1976) 59-64.
2. [2]. O. Redlich, J.N.S. Kwong, On the thermodynamics of solutions V: an equation of state fugacities of gaseous solutions, Chem. Rev. 44 (1949) 233-244.
3. [3]. B. Abolpour, A semi-empirical equation of state of saturated liquids, Fluid Phase Equilibria 388 (2015) 71-77.
4. [4]. G. Soave, Equilibrium constants from a modified Redlich-Kwong equation of state, Chem. Eng. Sci. 27 (1972) 1197-1203.
5. [5] B.I. Lee, M.G. Kesler, A generalized thermodynamic correlation based on three-parameter corresponding states, AICHE J. 21 (3) (1975) 510-527.
6. [6]. B. Abolpour, Investigating effects of molecular structure on the behavior of saturated liquid hydrocarbons using a novel semi-empirical equation of state, Fluid Phase Equilibria 456 (2018) 184-192.
7. [7]. E.A. Mason, T.H. Spurling, The Virial Equation of State, Pergamon Press, Oxford (1969).
8. [8]. J.D. Van der Waals, Over de continuiteit van den gas-en vloeistoftoestand (on the continuity of the gas and liquid state). Ph.D. Thesis, University of Amsterdam, Amsterdam, Netherlands, 1873.

9. [9]. J.C. Maxwell, On the Dynamical Theory of Gases, J Philosophical Transactions of the Royal Society of London, 157 (1867) 49–88.
10. [10]. L.D. Landau, E.M. Lifshitz, Mechanics (3rd ed.). Pergamon Press, Oxford, New York, USA, 1976.
11. [11]. J.D. Sally, P.J. Sally, Roots to research: a vertical development of mathematical problems, American Mathematical Society Bookstore, 2007.
12. [12]. J.M. Smith and H.C. Van Ness, Introduction to chemical engineering thermodynamics, McGraw-Hill, New York, 1988.
13. [13]. J.C. Lagarias, J.A. Reeds, M.H. Wright, P.E. Wright, Convergence properties of the nelder-mead simplex method in low dimensions, SIAM J. Optim., 9(1) (1998) 112-147.