International Journal of Thermophysics

, Volume 35, Issue 5, pp 783–811 | Cite as

A New Functional Form for Equations of State for Some Weakly Associating Fluids

Article

Abstract

A new functional form for equations of state for polar and weakly associating fluids was developed. It was established with a simultaneous optimization algorithm developed previously. As a result, equations of state in terms of the Helmholtz energy as a function of temperature and density were developed for hydrogen chloride (HCl) valid within \(T =\) (155–330) K and pressures up to \(p = 20\) MPa, diethyl ether (DEE) valid within \(T =\) (270–500) K and pressures up to \(p = 40\) MPa, and methyl chloride (R40) valid within \(T =\) (230–630) K and pressures up to \(p =\) 100 MPa. Those equations can be used for the calculation of all thermodynamic properties, including density, internal energy, enthalpy, heat capacity, speed of sound, saturation properties, etc.

Keywords

Diethyl ether Equation of state Functional form  Helmholtz energy Hydrogen chloride Methyl chloride  Thermodynamic properties 

List of Symbols

Latin Symbols

\(a\)

Specific Helmholtz energy (J \(\cdot \) kg\(^{-1}\))

AAD

Average absolute relative deviation (%)

\(b\)

Coefficient of the equation for the reduced Helmholtz energy of the ideal gas(–)

\(c\)

Specific heat capacity (J \(\cdot \) kg\(^{-1}\cdot \)K\(^{-1}\))

Coefficient of the \(c_{p}^{\mathrm{o}}\)and \(c_{v}^{\mathrm{o}}\) equation (–)

\(d\)

Density exponent of the equation for the reduced residual Helmholtz energy (–)

\(h\)

Specific enthalpy (J \(\cdot \) kg\(^{-1}\))

\(I\)

Number of terms

\(k\)

Integration constants for the reduced Helmholtz energy of the ideal gas

\(l\)

Density exponent of the exponential part for the reduced residual Helmholtz energy (–)

\(M\)

Molar mass (g \(\cdot \) mol\(^{-1}\))

\(n\)

Coefficient of the equation for the reduced residual Helmholtz energy (–)

Number of data points (–)

\(p\)

Pressure (MPa)

\(R\)

Molar gas constant (J\(\cdot \)mol\(^{-1}\,\cdot \) K\(^{-1}\))

\(s\)

Specific entropy (J \(\cdot \) kg\(^{-1}\,\cdot \, \)K\(^{-1}\))

\(t\)

Temperature exponent of the equation for the reduced residual Helmholtz energy (–)

\(T\)

Temperature (K)

\(w\)

Speed of sound (m \(\cdot \) s\(^{-1}\))

\(X\)

Relative deviation (%)

Greek Symbols

\(\alpha \)

Reduced Helmholtz energy (–)

\(\beta \)

Gaussian bell-shaped parameter (–)

\(\gamma \)

Gaussian bell-shaped parameter (–)

\(\delta \)

Reduced density (–)

\(\varepsilon \)

Gaussian bell-shaped parameter (–)

\(\eta \)

Gaussian bell-shaped parameter (–)

\(\rho \)

Density (kg \(\cdot \) m\(^{-3}\))

\(\tau \)

Reciprocal reduced temperature (–)

Subscript

B

Boiling point

c

Critical

calc

Calculated by the equation of state

Evap

Vaporization

exp

Experimental

GB

Gaussian bell-shaped

\(p\)

Isobaric

PE

Planck–Einstein

pol

Polynomial

s

Saturation

tr

Triple point

\(v\)

Isochoric

Superscript

\(\prime \)

Saturated liquid

\(\prime \prime \)

Saturated vapor

o

Ideal

r

Residual

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.ThermodynamicsRuhr-Universitaet BochumBochumGermany
  2. 2.Hansa Consult Ingenieurgesellschaft mbHReinbekGermany

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