http://orcid.org/0000-0003-3171-6362
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ABSTRACT
A new generalized perturbed thermodynamic nonlinear isotherm regularity (GPTNLIR) equation of state (EoS) has been proposed for the fluids over the entire density range from gas to liquid. The GPTNLIR has been derived on the basis of an effective nearest neighbor pair interaction of an extended average effective pair potential (AEPP) in the framework of the thermodynamic perturbation theory (TPT). The selected AEPP is an extended Lennard-Jones (12, 6, 3) type which considers the repulsive, dispersion, dipole-dipole and longer-range interactions between pair molecules, respectively. Based on the EoS, a non-linear relationship exists between (Z– ZCS)v2 and ρ for each isotherm of fluid, where Zis the compression factor, v=1/ρis the molar volume, ZCS is Carnahan–Starling (CS) expression for the compression factor of the reference fluid with the temperature-dependent effective hard-core diameter (σeff). The validity of EoS against the experimental p–v–Tdata were tested for a variety of fluids, including polar, non-polar, hydrogen bonded and quantum fluids. This EoS provides the estimation of σeff at T>Tc, T=Tc and T<Tc, in which Tc is critical temperature, for each real fluid using its experimental p–v–T data and the extension of TPT theory as well.
Acknowledgement
We are indebted to the Research Council of the Isfahan University of Technology (IUT) for their support of this work.
Disclosure statement
No potential conflict of interest was reported by the authors.
Nomenclature
| Ci(T) | = | = parameters of model |
| kB | = | = Boltzmann constant |
| N | = | = number of particle |
| p | = | = pressure |
| pint | = | = the internal pressure, |
| R | = | = gas constant |
| = | = average of nearest neighbouring separation | |
| T | = | = temperature in K |
| TC | = | = critical temperature |
| U | = | = total configuration potential energy |
| = | = the reference contribution of average effective pair potential | |
| = | = the perturbation contribution of average effective pair potential | |
| = | = hard-sphere potential | |
| v | = | = molar volume |
| Z | = | = compression factor |
| ZCS | = | = Carnahan–Starling equation of state |
| = | = compression factor of the reference fluid | |
| = | = compression factor of the perturbation | |
| φ | = | = average coordination number |
Greek letters
| η | = | = packing fraction |
| ρ | = | = molar density |
| ρBoyle | = | = Boyle density |
| σeff | = | = effective hardcore diameter in Å |
| ω | = | = integral constant |
Subscripts
| calc. | = | = calculated index |
| C | = | = critical index |
| exp. | = | = experimental index |
| int | = | = internal index |
| T | = | = temperature index |
Superscripts
| (0) | = | = reference system index |
| (1) | = | = perturbed system index |
| id | = | = ideal gas index |
| max | = | = maximum index |
| min | = | = minimum index |
| non-id | = | = non-ideal gas index |