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.
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Abbreviations
- A :
-
Helmholtz energy
- B :
-
2nd virial coefficient
- C p :
-
Isobaric heat capacity
- C V :
-
Isochoric heat capacity
- c :
-
Chain length parameter of the SPHCT EOS
- d :
-
Apparent hard-sphere diameter
- d 0 :
-
d at zero density
- H :
-
Enthalpy
- h :
-
Planck’s constant
- k B :
-
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
- α p :
-
Isobaric thermal expansivity
- δ :
-
Perturbation theory integral, Eq. 20
- \({\epsilon}\) :
-
Lennard-Jones potential energy parameter
- κ T :
-
Isothermal compressibility
- Λ:
-
Thermal de Broglie wavelength
- π T :
-
Internal pressure
- ρ :
-
Density
- σ :
-
Lennard-Jones potential size parameter
- ξ :
-
Reduced density
- att:
-
Attraction
- c:
-
Critical
- hs:
-
Hard sphere
- m:
-
Molar property
- r:
-
Residual property
- \({{\tilde{}}}\) :
-
Reduced property
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Boshkova, O.L., Deiters, U.K. Soft Repulsion and the Behavior of Equations of State at High Pressures. Int J Thermophys 31, 227–252 (2010). https://doi.org/10.1007/s10765-010-0727-7
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DOI: https://doi.org/10.1007/s10765-010-0727-7