Thermodynamic Properties of Fluids from Speed of Sound: Integration Along Isentropes

Year 2022, Volume: 25 Issue: 1, 96 - 107, 01.03.2022

Muhamed Bijedic Enver đidić

https://doi.org/10.5541/ijot.986170

Abstract

The equations connecting speed of sound with other thermodynamic properties of gases and liquids, suitable for numerical integration with respect to temperature, density, and pressure, along isentropes, are derived. Algorithms of their solution are given too. They are tested with several substances (e.g., Ar, N2, O2, CH4, CO2, and H2O) in wide ranges of pressure and temperature. Average absolute deviation of thermal properties is 0.0129% in supercritical gaseous phase, 0.0308% in transcritical gaseous phase, and 0.0009% in liquid phase. Corresponding deviations of caloric properties are 0.1706%, 0.1863%, and 0.0702%, respectively.

Keywords

Thermodynamic properties, fluids, speed of sound, entropy

References

• M. Bijedić, N. Neimarlija, “Thermodynamic Properties of Gases from Speed-of-Sound Measurements,” Int. J. Thermophys., 28, 268-278, 2007.
• M. Bijedić, N. Neimarlija, “Thermodynamic Properties of Carbon Dioxide Derived from the Speed of Sound,” J. Iran. Chem. Soc., 5, 286-295, 2008.
• Estrada-Alexanders, A. F. (1996). Thermodynamic Properties of Gases from Measurements of the Speed of Sound (Doctoral dissertation), Imperial College, London, UK.
• M. Bijedić, N. Neimarlija, “Speed of Sound as a Source of Accurate Thermodynamic Properties of Gases,” Lat. Am. Appl. Res., 43, 393-398, 2013.
• M. Bijedić, S. Begić, “Thermodynamic Properties of Vapors from Speed of Sound,” J. Thermodyn., 2014, 1-5, 2014.
• M. Bijedić, N. Neimarlija, “Thermodynamic Properties of Liquids from Speed of Sound Measurements,” Int. J. Thermodyn., 15, 61-68, 2012.
• M. Bijedić, S. Begić, “Density and Heat Capacity of Liquids from Speed of Sound,” J. Thermodyn., 2016, 1-8, 2016.
• A. F. Estrada-Alexanders, Justo, D., “New Method for Deriving Accurate Thermodynamic Properties from Speed-of-Sound,” J. Chem. Thermodyn., 36, 419-429, 2004.
• M. Bijedić, S. Begić, “Solution of the Adiabatic Sound Wave Equation as a Nonlinear Least Squares Problem,” Int. J. Thermophys., 40, 1-36, 2019.
• M. J. Moran, H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 5th Ed. Chichester: John Wiley & Sons, 2006.
• W. Chenney, D. Kincaid, Numerical Mathematics and Computing, 6th Ed. Belmont: Thomson Brooks/Cole, 2008.
• C. de Boor, A Practical Guide to Splines. New York: Springer, 1978.
• G. H. Golub, C. F. Van Loan, Matrix Computations. Baltimore: Johns Hopkins University Press, 1983.
• T. E. Hull, W. H. Enright, and K. R. Jackson, User's Guide for DVERK – A Subroutine for Solving Non-Stiff ODEs. University of Toronto, 1976.
• K. Levenberg, “A Method for the Solution of Certain Non-Linear Problems in Least Squares,” Q. Appl. Math., 2, 164-168, 1944.
• D. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” SIAM J. Appl. Math., 11, 431-441, 1963.
• J.J. Moré, B.S. Garbow, and K.E. Hillstrom, User Guide for MINPACK-1. Argonne National Laboratory Report ANL-80-74, 1980.
• C. Tegeler, R. Span, and W. Wagner, “A New Equation of State for Argon Covering the Fluid Region for Temperature from the Melting Line to 700 K at Pressures up to 1000 MPa,” J. Phys. Chem. Ref. Data, 28, 779-850, 1999.
• R. Span, E. W. Lemmon, R. T. Jacobsen, W. Wagner, and A. Yokozeki, “A Reference Equation of State for the Thermodynamic Properties of Nitrogen Covering the Fluid Region for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa,” J. Phys. Chem. Ref. Data, 29, 1361-1433, 2000.
• R. Schmidt, W. Wagner, “A New Form of the Equation of State for Pure Substances and Its Application to Oxygen,” Fluid Phase Equilibria, 19, 175-200, 1985.
• R. B. Stewart, R. T. Jacobsen, and W. Wagner, “Thermodynamic Properties of Oxygen from the Triple Point to 300 K with Pressures to 80 MPa,” J. Phys. Chem. Ref. Data, 20, 917-1021, 1991.
• U. Setzmann, W. Wagner, “A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K and Pressures up to 1000 MPa,” J. Phys. Chem. Ref. Data, 20, 1061-1125, 1991.
• R. Span, W. Wagner, “A New Equation of State for Carbon Dioxide Covering the Fluid Region for Temperature from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa,” J. Phys. Chem. Ref. Data, 25, 1509-1596, 1996.
• W. Wagner, A. Pruss, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data, 31, 387-535, 2002.
• D. Y. Peng, D. B. Robinson, “A New Two-Constant Equation of State,” Ind. Eng. Chem. Fund., 15, 59-64, 1976.
• S. Lago, P. A. Giuliano Albo, “A Recursive Equation Method for the Determination of Density and Heat Capacity: Comparison Between Isentropic and Isothermal Integration Paths,” J. Chem. Thermodyn., 42, 462-465, 2010.