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Scaling Models of thermodynamic properties for the diethyl ether at the saturation


I. Abdulagatov1, E. Ustjuzhanin2, V. Shishakov2, P. Popov2, J. Wu3 and Y. Zhou3

1Geothermal Research Institute of the Dagestan Scientific Center RAS, Makhachkala, Russia
2Moscow Power Engineering Institute (Technical University), Moscow, Russia
3Xi'an Jiaotong University, Xi'an, P.R. China

Keywords: coexistence curve, scaling theoryliquid density, gas density, saturation pressure, critical exponents, critical point
property: liquid density, gas density, saturation pressure, derivatives
material: diethyl ether

New experimental data by Abdulagatov et al. [1] on saturated properties, F = (the saturated densities, ρl, ρg, the vapor pressure, Ps) of the diethyl ether (DEE) are analyzed using various scaling models. The experimental values of (ρlρg,T) are used to be compared with some models those represent F = (ρl, ρg, the order parameter, fs, the coexistence curve diameter, fd). We have considered equations suggested by Wegner, 1980, Fisher et al, 2000, Abdulagatov et al., 2010, and other models related to F = (ρl, ρg, fs, fd).

A new analytical form to express F is studied. It has a combined structure [2] with scaling and regular parts

F(τ,D,B) = F(τ,D,B1)scale + F(τ,B2)reg ,                                               (1)

here τ = (Tc - T)/Tc – reduced temperature, D = a,β, …) - critical characteristics and B are coefficients.

Combined models of F = (fs, fd) have the form [2]

fs = Bs0τ β + Bs1τ β + Bs2τ β+ + Bs3τ 2+ Bs4τ 3,                               

fd = Bd0τ 1-a+ Bd1τ 1-a+Δ + Bd2τ 1-a++ Bd3τ 2+ Bd4τ 3,          (2)

here Δ – non-asymptotic critical exponent (a Wegner correction).

Combined models of F = (ρl,ρg) can be expressed with the Eq. (2) in the form

ρl = (fd + fs+1) ρc,        ρg = (fd - fs+1) ρc .                                              (3)

Adjustable coefficients, B, and characteristics D = (a,β,Tc,) are determined by fitting combined models to the input data sets of DEE with the help of a non linear method.

We have considered equations suggested by Wagner, 1973, Xiang and Tan, 1994, and Wu et al., 2005, Abdulagatov et al., 2011, and other models those can describe F = Ps. A combined model (1) is built in the form [2] to represent experimental (Ps,T)exp – data for DEE.

Some application results are determined and discussed. They are got with the help of the models and connected with thermodynamic properties on the coexistence curve of DEE. The work is supported by RFBR.

References
  1. N.G. Polikhronidi, I.M. Abdulagatov, R.G. Batyrova, G.V. Stepanov, E.E. Ustuzhanin, J.T. Wu. Int. J. Thermophys. 32, 189 (2011)

  2. Ustjuzhanin E.E., V.F. Utenkov, V.A. Rykov. Soft matter under exogenic impact. NATO Science series. Part II, Vol. 242. Editor Rzoska S. Eddition - Springer, The Netherlands, (2006)

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