Abstract
An equation of state is developed for the Lennard-Jones model fluid, truncated and shifted at \(r_{\mathrm{c}} = 2.5\sigma \). The underlying dataset contains thermodynamic properties at 706 state points including pressure, residual internal energy, first volume derivative of the residual internal energy, and residual isochoric heat capacity as a function of temperature and density. The equation of state is explicit in terms of the Helmholtz energy, allowing the determination of any thermodynamic property by differentiation. It is valid for temperatures \(0.6<T/T_{\mathrm{c}}<10\) and pressures \(p/p_{\mathrm{c}}<70\). High accuracy and good extrapolation behavior of the equation of state are established.
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Abbreviations
- \(a\) :
-
Helmholtz energy
- \(c_{1, }c_{2 }\) :
-
Integration constants of the ideal Helmholtz energy
- \(c_{v }\) :
-
Isochoric heat capacity
- \(d_{i}\) :
-
Density exponents of the residual Helmholtz energy
- \(h\) :
-
Enthalpy
- \(l_{i}\) :
-
Density exponents of the exponential term of the residual Helmholtz energy
- \(m\) :
-
Molecular mass
- \(N\) :
-
Number of molecules in the simulation
- \(n_{i}\) :
-
Coefficients of the residual Helmholtz energy
- \(N_{i}\) :
-
Coefficients of the ancillary equations
- \(p\) :
-
Pressure
- \(r\) :
-
Radius
- \(r_{\mathrm{c}}\) :
-
Cut-off radius
- \(s\) :
-
Entropy
- \(t\) :
-
Time
- \(T\) :
-
Temperature
- \(t_{i}\) :
-
Temperature exponents of the residual Helmholtz energy
- \(u\) :
-
Potential energy/internal energy
- \(V\) :
-
Volume
- \(X\) :
-
Any thermodynamic property
- \(\alpha \) :
-
Reduced Helmholtz energy
- \(\beta _{i}\) :
-
Gaussian bell-shaped parameters
- \(\gamma _{i}\) :
-
Gaussian bell-shaped parameters
- \(\delta \) :
-
Reduced density
- \(\varepsilon \) :
-
Energy parameter of the molecular model
- \(\varepsilon _{i}\) :
-
Gaussian bell-shaped parameters
- \(\eta _{i}\) :
-
Gaussian bell-shaped parameters
- \(\theta \) :
-
\((1 - T/T_{\mathrm{c}})\) for the ancillary equations
- \(\rho \) :
-
Density
- \(\sigma \) :
-
Size parameter of the molecular model
- \(\tau \) :
-
Inverse reduced temperature
- c:
-
Critical
- LJ:
-
Lennard-Jones
- LJTS:
-
Lennard-Jones truncated and shifted
- v:
-
Vapor
- \(v\) :
-
Isochoric
- 0:
-
Reference
- o:
-
Ideal
- r:
-
Residual
- \(\prime \) :
-
Saturated liquid
- \(\prime \prime \) :
-
Saturated vapor
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Acknowledgments
We thank E. W. Lemmon for his support during the development of the equation of state and G. Guevara-Carrion for her support in carrying out molecular simulation work. This project was funded by the Deutsche Forschungsgemeinschaft (DFG).
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Thol, M., Rutkai, G., Span, R. et al. Equation of State for the Lennard-Jones Truncated and Shifted Model Fluid. Int J Thermophys 36, 25–43 (2015). https://doi.org/10.1007/s10765-014-1764-4
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DOI: https://doi.org/10.1007/s10765-014-1764-4