An equation of state based upon a ratio of polynomials (rational) form for the residual Helmholtz energy: application to nitrogen, argon and methane¹

¹Contribution of the National Institute of Standards and Technology, not subject to copyright in the U.S. Commercial equipment, instruments, or materials are identified only in order to adequately specify certain procedures. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products identified are necessarily the best available for the purpose.

ABSTRACT

This work presents an equation of state that contains the residual Helmholtz free energy as a ratio of polynomials in density with temperature-dependent coefficients and demonstrates that it is a viable alternative for describing thermodynamic properties accurately. The specific form of the equation in this work has six density terms in the numerator, three density terms in the denominator, and five temperature parameters for each temperature-dependent coefficient. Nitrogen, argon, and methane serve as prototype fluids to demonstrate the capability of the form to describe p–ρ–T behaviour, vapour pressures, speeds of sound, and isochoric heat capacities up to 1000 MPa. Characteristic curves for several properties of nitrogen generated using the equation exhibit proper behaviour at high temperatures and pressures. Because the equation contains no exponential terms or non-integer exponents, the computational time associated with the new equation is more than a factor of 10 less than that required for similar equations with comparable accuracy.

KEYWORDS:

• Equation of state
• nitrogen
• argon
• methane
• ratio of polynomials

Acknowledgments

The authors thank Prof. Johann Fischer for many helpful and stimulating discussions. They also thank Dr Eric Lemmon of NIST, Boulder, for his assistance and suggestions during the development of this EOS.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors acknowledge support for this work from the Jack E. & Frances Brown Chair endowment at Texas A&M University; the Texas Engineering Experiment Station.