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International Journal of Thermophysics

, Volume 31, Issue 2, pp 227–252 | Cite as

Soft Repulsion and the Behavior of Equations of State at High Pressures

  • Olga L. Boshkova
  • Ulrich K. Deiters
Article

Abstract

The so-called characteristic curves of Brown—the Amagat (Joule inversion), Boyle, and Charles (Joule–Thomson inversion) curves—of hydrogen are calculated with several equations of state. This work demonstrates that not all equations can generate physically reasonable Amagat curves. After inclusion of corrections for soft repulsion (based on the Weeks–Chandler–Andersen perturbation theory) and quantum effects into the simplified perturbed-hard-chain theory (SPHCT) equation of state, this equation is able to not only generate an Amagat curve, but also predict pVT data, residual Gibbs energies, and heat capacities of several gases at and above 100 MPa reasonably well.

Keywords

Equation of state Perturbation theory Soft repulsion Joule inversion curve Amagat curve Brown’s characteristic curves Hydrogen 

List of symbols

A

Helmholtz energy

B

2nd virial coefficient

Cp

Isobaric heat capacity

CV

Isochoric heat capacity

c

Chain length parameter of the SPHCT EOS

d

Apparent hard-sphere diameter

d0

d at zero density

H

Enthalpy

h

Planck’s constant

kB

Boltzmann’s constant

m

Molecular mass; chain length parameter of the PC-SAFT EOS

N

Number of molecules

n

Amount of substance

p

Pressure

R

Universal gas constant

r

Intermolecular distance

T

Temperature

U

Internal energy

u

Pair potential

V

Volume

v*

EOS size parameter

y

Background correlation function

Z

Compressibility factor

αp

Isobaric thermal expansivity

δ

Perturbation theory integral, Eq. 20

\({\epsilon}\)

Lennard-Jones potential energy parameter

κT

Isothermal compressibility

Λ

Thermal de Broglie wavelength

πT

Internal pressure

ρ

Density

σ

Lennard-Jones potential size parameter

ξ

Reduced density

Subscripts

att

Attraction

c

Critical

hs

Hard sphere

m

Molar property

Superscripts

r

Residual property

\({{\tilde{}}}\)

Reduced property

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute of Physical ChemistryUniversity of CologneKölnGermany

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