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The Characteristic Curves of Water

  • Arnold Neumaier
  • Ulrich K. Deiters
Article
  • 199 Downloads

Abstract

In 1960, E. H. Brown defined a set of characteristic curves (also known as ideal curves) of pure fluids, along which some thermodynamic properties match those of an ideal gas. These curves are used for testing the extrapolation behaviour of equations of state. This work is revisited, and an elegant representation of the first-order characteristic curves as level curves of a master function is proposed. It is shown that Brown’s postulate—that these curves are unique and dome-shaped in a double-logarithmic pT representation—may fail for fluids exhibiting a density anomaly. A careful study of the Amagat curve (Joule inversion curve) generated from the IAPWS-95 reference equation of state for water reveals the existence of an additional branch.

Keywords

Brown’s characteristic curve Ideal curve IAPWS-95 equation of state Joule inversion Joule–Thomson inversion Water 

Symbols

\(B_i\)

ith virial coefficient

\(C_p\)

Isobaric heat capacity

\(C_V\)

Isochoric heat capacity

\(c_X\)

(Dimensionless) thermodynamic response function, \(X \in \{p, V, T, \kappa \}\) (Eqs. 1415)

G

Gibbs energy

\(\varvec{G}\)

Hessian of \(G_\mathrm{m}(p, T)\)

H

Configurational enthalpy

n

Amount of substance

p

Pressure

\(q_X\)

Dimensionless logarithmic slope, \(X \in \{\mathrm{A, B, C}\}\) (Eqs. 1618)

R

Universal gas constant

S

Configurational entropy

T

Temperature

U

Configurational internal energy

V

Volume

Z

Compression factor, \(Z = p V_\mathrm{m}/(R T)\)

\(\alpha _p\)

Isobaric thermal expansivity

\(\kappa _T\)

Isothermal compressibility

\(\rho \)

Molar density, \(\rho = V_\mathrm{m}^{-1}\)

Subscripts

\(\mathrm{A}\)

Amagat (Joule inversion) curve

\(\mathrm{B}\)

Boyle curve

\(\mathrm{c}\)

Critical property

\(\mathrm{C}\)

Charles (Joule–Thomson inversion) curve

\(\mathrm{m}\)

Molar property

Superscripts

\(\mathrm{id}\)

Ideal gas

\(\mathrm{g}\)

Vapour phase

\(\mathrm{l}\)

Liquid phase

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ViennaWienAustria
  2. 2.Institute of Physical ChemistryUniversity of CologneKölnGermany

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