A scaling equation of state near the critical point and the stability boundary of a liquid

Bezverkhii, P. P.; Martynets, V. G.; Matizen, É. V.

doi:10.1134/s1810232807030083

Cited by 8 publications

(5 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The physical basis for the application of scaling equations of state, as well as the entire theory of scaling, consists in taking into account the collective interactions of developed fluctuations at the secondorder phase transition point. It leads to a singular behavior of thermodynamic deriva tives (in particular, heat capacity) with noninteger critical exponents, which was discovered in the experiment [7].…”

Section: Modified Coefficients A(t)_2ph and A(t)_scr Use In Rka Equat...mentioning

confidence: 90%

“…The method for determination the near critical pressure was based on the modified RedlichKwongAungier (RKA) equation of state [10] as regular part and the scaling equa tion of state from [7]. As the crossover function between the regular and the scaling parts is used the classical function of the extinction probability of temperature and density fluctua tions from [7]. In paper [11] was presented the method to determine the main thermodynamics properties in the two phase region of the carbon dioxide.…”

Section: Methodsmentioning

confidence: 99%

“…The regular part of equation of state (RedlichKwong Aungier EoS -RKA EoS), which is connected with the scaling part of equation of state with the crossover function. As the crossover function between the regular and the scaling parts is used the classical function of the extinc tion probability of the temperature and of the density fluctuations from [7]:…”

Section: Modified Coefficients A(t)_2ph and A(t)_scr Use In Rka Equat...mentioning

confidence: 99%

“…The most wellknown reference tables [5] are calculated for CO 2 by a multiconstant regular Span and Wagner EoS (SW EoS, 58 adjustable constants and 35 different powerlaw indices). Articles [6,7] represent the thermal combined equation of state, including a new 11constant EoS for the regular region and scaling 6constant EoS for the critical region of states, a unifed description of the thermal and caloric properties of carbon dioxide and for helium. In paper [8] proposes the crossover cubicplusassociation equation of state.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Modification of scaled equation of state to determine the pressure in the CO2 critical region

Vorobieva

2022

TAPR

View full text Add to dashboard Cite

The object of the research is carbon dioxide and its pressure distribution depending on the range of temperature and density in the region of the critical point. One of the most problematic areas of methods for finding thermodynamic parameters of a real gas is insufficient accuracy in calculations in the places of occurrence and rapid development of fluctuation phenomena, which are inherent in phase transitions of the first and second terms. For a more detailed and accurate description of the nature of the thermodynamic parameters in the region of the critical point, scaling and crossover equations of state were developed. Such equations, due to the presence of regular and scaling parts, allow describing the thermodynamic parameters of a real gas not only directly near the critical point, but also at some distance from it, maintaining a small error relative to experimental data. The article proposes an equation of state, which contains a scaling part described according to the rules of statistical physics, and a regular part in the form of a classical cubic equation of state. The equation is used to calculate the pressure of carbon dioxide in the region around the critical point from 300 K to 305 K. The article proposes a correlation equation for the scaling correction of the regular part (Redlich-Kwong-Aungier model) of the crossover equation of state, which is related to the scaling part the equation of state is a crossover function. The obtained results for the pressure in the critical region showed good agreement with the baseline data. The error relative to the experimental data is halved compared to the original model of the Redlich-Kwong-Aungier equation. The obtained results ensure the applicability of the proposed method in the temperature range from 300 K to 305 K. Due to the simplicity of the form of the regular equation of state and the small number of empirical coefficients for the large-scale equation of state, the obtained method can be used for practical problems of computational hydrodynamics without spending a lot of computing time.

show abstract

Section: Modified Coefficients A(t)_2ph and A(t)_scr Use In Rka Equat...mentioning

confidence: 90%

Section: Methodsmentioning

confidence: 99%

Section: Modified Coefficients A(t)_2ph and A(t)_scr Use In Rka Equat...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modification of scaled equation of state to determine the pressure in the CO2 critical region

Vorobieva

2022

TAPR

View full text Add to dashboard Cite

show abstract

“…A scaling equation of state, having four system dependent constants and explicitly describing the pressure and heat capacity of fluids in a rather wide range of density around their critical points with an accuracy comparable to the experimental, was obtained in [28][29][30]. To describe regular behavior in a wide range of thermodynamic parameters, a physi cally reasonable equation of state is required, which would have an optimal number of adjustable parame ters, sufficient to approximate the experimental data with the least possible error.…”

Section: Introductionmentioning

confidence: 99%

Description of heat capacity C v of simple liquids using a thermal equation of state including regular and scaling parts

2015

Self Cite

View full text Add to dashboard Cite

The p,ρ,T data for CO 2 are approximated in the ranges of 0 < ρ/ρ c <2, 217 < T < 430 K, and 0 < p ≤ 25 MPa and for SF 6 in the ranges of 0 < ρ/ρ c < 2.5, 225 < T < 340 K, and 0 < p ≤ 10 MPa using a new unified equation of state. In this equation, pressure p is an explicit function of ρ and T. It includes a new reg ular part to approximate p,ρ,T data in the liquid and gaseous regions of state outside the critical region, a sin gular part that is a scaling equation of state for the critical region, and a crossover function for combining these equations. The regular part consists of the sum of eight terms with eight constants, three of which are deter mined by the conditions at the critical point. The total number of system dependent constants is fourteen, including the critical values of p, ρ, and T. In the scaling part of the equation of state, the critical exponents of the three dimensional Ising model are used. The mean square error of the description by pressure of the p,ρ,T data for CO 2 is ±0.63%, and for the p,ρ,T data obtained for SF 6 , it is ±0.70% over the entire range of gas and liquid states. Using the constants of the combined equation, heat capacity C v is calculated at isoch ores, isotherms, and a binodal, including those in the critical region. The calculation results describes the known experimental data of C v with an error of ±8%.

show abstract

Combined equation of liquid and gas states, including classical and scaling parts

Bezverkhy

Martynets

Matizen

2009

Journal of Molecular Liquids

View full text Add to dashboard Cite

A scaling equation of state near the critical point and the stability boundary of a liquid

Cited by 8 publications

References 9 publications

Modification of scaled equation of state to determine the pressure in the CO2 critical region

Modification of scaled equation of state to determine the pressure in the CO2 critical region

Description of heat capacity C v of simple liquids using a thermal equation of state including regular and scaling parts

Combined equation of liquid and gas states, including classical and scaling parts

Contact Info

Product

Resources

About