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A Method for the Selection of a Functional Form for a Thermodynamic Equation of State Using Weighted Linear Least Squares Stepwise Regression

  • R. T. Jacobsen
  • R. B. Stewart
  • R. W. CrainJr.
  • G. L. Rose
  • A. F. Myers
Part of the Advances in Cryogenic Engineering book series (ACRE, volume 21)

Abstract

In studies to determine equations of state for thermodynamic fluids, a number of polynomial forms have been suggested for use in fitting experimental measurements. The purpose of this study was to develop a method for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented here were developed for use in the determination of an equation of state for oxygen and nitrogen. However, these methods are generally applicable in studies for determining an optimum polynomial equation for fitting to a large number of data points. The equation of state derived for oxygen and nitrogen [1] has subsequently been applied to additional fluids by others (e.g., by McCarty [2]) for methane and appears to be useful for many fluids. The statistical analysis of the results of the least squares fit to determine a thermodynamic equation of state should be considered an adjunct to the calculation of properties from the formulation for direct comparison to experimental data to determine the quality of the representation of the data.

Keywords

Critical Region Stepwise Regression Stepwise Multiple Regression Adjustable Coefficient Thermodynamic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. T. Jacobsen, R. B. Stewart, and A. F. Myers, in: Advances in Cryogenic Engineering, Vol. 18, Plenum Press, New York (1973), p. 248.Google Scholar
  2. 2.
    R. D. McCarty, Cryogenics 14(5):276 (1974).CrossRefGoogle Scholar
  3. 3.
    T. R. Strobridge, NBS Tech. Note 129A (1963).Google Scholar
  4. 4.
    G. L. Rose, M.S. Thesis, University of Idaho, Moscow, Idaho (1974).Google Scholar
  5. 5.
    R. T. Jacobsen, Ph.D. Dissertation, Washington State University, Pullman, Washington (1972).Google Scholar
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    R. B. Stewart and R. T. Jacobsen, Cryogenics 13(9):526 (1973).CrossRefGoogle Scholar
  7. 7.
    R. B. Stewart, R. T. Jacobsen, and A. F. Myers, “The Thermodynamic Properties of Oxygen and Nitrogen: Part I—Thermodynamic Properties of Nitrogen from 115 R to 3500 R with Pressures to 150,000 psia; Part II—Thermodynamic Properties of Oxygen from 100 R to 600 R with Pressures to 5000 psia”; Part I: NASA-CR-128527 (N72–30957); Part II: NASA-CR-128528 (N72–30958). (Available from National Technical Information Service, Springfield, Virginia 22151.)Google Scholar
  8. 8.
    R. T. Jacobsen and R. B. Stewart, J. Phys. Chem. Ref. Data 2(4):757 (1973).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1960

Authors and Affiliations

  • R. T. Jacobsen
    • 1
  • R. B. Stewart
    • 1
  • R. W. CrainJr.
    • 2
  • G. L. Rose
    • 3
  • A. F. Myers
    • 4
  1. 1.University of IdahoMoscowUSA
  2. 2.Washington State UniversityPullmanUSA
  3. 3.McKellip Engineering, Inc.BoiseUSA
  4. 4.Computation and Simulation DivisionNASA Flight Research CenterEdwardsUSA

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