Equations of State for Cu, Ag, and Au for Wide Ranges in Temperature and Pressure up to 500 GPa and Above

2001 ◽  
Vol 30 (2) ◽  
pp. 515-529 ◽  
Author(s):  
W. B. Holzapfel ◽  
M. Hartwig ◽  
W. Sievers
Keyword(s):  
Equations Of State ◽  
Temperature And Pressure

scholarly journals Group additivity calculation of the standard molal thermodynamic properties of aqueous amino acids, polypeptides and unfolded proteins as a function of temperature, pressure and ionization state

2005 ◽  
Vol 2 (5) ◽  
pp. 1515-1615 ◽  
Author(s):  
J. M. Dick ◽  
D. E. LaRowe ◽  
H. C. Helgeson
Keyword(s):  
Amino Acids ◽  
Thermodynamic Properties ◽  
Equations Of State ◽  
Reference Model ◽  
Accurate Determination ◽  
Group Additivity ◽  
Unfolded Proteins ◽  
Ionization State ◽  
Degree Of Ionization ◽  
Temperature And Pressure

Abstract. Thermodynamic calculation of the chemical speciation of proteins and the limits of protein metastability affords a quantitative understanding of the biogeochemical constraints on the distribution of proteins within and among different organisms and chemical environments. These calculations depend on accurate determination of the ionization states and standard molal Gibbs free energies of proteins as a function of temperature and pressure, which are not generally available. Hence, to aid predictions of the standard molal thermodynamic properties of ionized proteins as a function of temperature and pressure, calculated values are given below of the standard molal thermodynamic properties at 25°C and 1 bar and the revised Helgeson-Kirkham-Flowers equations of state parameters of the structural groups comprising amino acids, polypeptides and unfolded proteins. Group additivity and correlation algorithms were used to calculate contributions by ionized and neutral sidechain and backbone groups to the standard molal Gibbs free energy (Δ G°), enthalpy (Δ H°), entropy (S°), isobaric heat capacity (C°P), volume (V°) and isothermal compressibility (κ°T) of multiple reference model compounds. Experimental values of C°P, V° and κ°T at high temperature were taken from the recent literature, which ensures an internally consistent revision of the thermodynamic properties and equations of state parameters of the sidechain and backbone groups of proteins, as well as organic groups. As a result, Δ G°, Δ H°, S° C°P, V° and κ°T of unfolded proteins in any ionization state can be calculated up to T~-300°C and P~-5000 bars. In addition, the ionization states of unfolded proteins as a function of not only pH, but also temperature and pressure can be calculated by taking account of the degree of ionization of the sidechain and backbone groups present in the sequence. Calculations of this kind represent a first step in the prediction of chemical affinities of many biogeochemical reactions, as well as of the relative stabilities of proteins as a function of temperature, pressure, composition and intra- and extracellular chemical potentials of O2 and H2, NH3, H2PO4 and CO2.

AN EQUATION OF STATE FOR GASES AT LOW DENSITIES

1932 ◽  
Vol 6 (6) ◽  
pp. 596-604 ◽  
Author(s):  
D. LeB. Cooper ◽  
O. Maass
Keyword(s):  
Carbon Dioxide ◽  
Equation Of State ◽  
Equations Of State ◽  
Absolute Temperature ◽  
Viscosity Function ◽  
Temperature And Pressure ◽  
New Equation ◽  
Molecular Radius ◽  
Expanded Form ◽  
Density Results

An equation of state for gases at low densities is developed, using a new function for the change in viscosity with temperature, also developed herein.The gas law equation takes the form[Formula: see text]or V(1 + KT)(PV − RT) = λT − a where a and b are constants corresponding to those of the Van der Waals' equation, and K is a constant derived from the proposed viscosity function which is, for carbon dioxide,[Formula: see text]where K is a constant and η is the viscosity at an absolute temperature T.In the case of carbon dioxide the equation was found to follow density results with an accuracy of from 0.01% to within experimental limits, and the viscosity function was found to agree with Sutherland's (10) results between −78.5 and 20 °C.Comparisons with several other equations of state are made. These show that the new equation is probably more accurate than any other.An expanded form of the new equation, namely:[Formula: see text]permits calculations of the slopes of isothermals for any temperature. Comparisons are made with experimental data.The expanded form of the equation may be solved for K, giving the expression:[Formula: see text]where [Formula: see text] and [Formula: see text] and ξ = Rb0, and since the equation enables the calculation of the molecular radius r, the viscosity may be calculated for any temperature and pressure over which the equation holds.

Modeling Approaches to Hydration Properties of Aqueous Nonelectrolytes at Elevated Temperatures and Pressures

2008 ◽  
Vol 73 (3) ◽  
pp. 322-343 ◽  
Author(s):  
Josef Sedlbauer
Keyword(s):  
Elevated Temperatures ◽  
Equations Of State ◽  
Environmental Chemistry ◽  
Hydrothermal Systems ◽  
Organic Solutes ◽  
Hydration Properties ◽  
New Developments ◽  
Elevated Pressures ◽  
Temperature And Pressure ◽  
Temperature Correlations

Thermodynamic models describing temperature and pressure evolution of Henry's law constant and related properties of hydration of aqueous nonelectrolyte solutes are reviewed. The included models cover a broad range spanning from simple van't Hoff-like equations used in environmental chemistry over the more elaborate empirical or semiempirical temperature correlations favored for engineering purposes to complete equations-of-state for hydration properties originating in the theory of near-critical phenomena and developed for modeling of hydrothermal systems. For aqueous organic solutes, the methods are often coupled with the group additivity approximation, leading to complex tools for predicting the properties of solutions containing organic species. The various models were subjected to tests documenting their expected range of applicability at elevated pressures (for acid gases) or at high temperatures (for hydrocarbons and oxygen-containing organic solutes). New developments in the field are discussed and some future needs are envisioned.

scholarly journals Condensed-matter equation of states covering a wide region of pressure studied experimentally

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Elijah E. Gordon ◽  
Jürgen Köhler ◽  
Myung-Hwan Whangbo
Keyword(s):  
Strain Energy ◽  
Equations Of State ◽  
Interatomic Potential ◽  
Condensed Matter ◽  
Mathematical Functions ◽  
Wide Region ◽  
Equation Of States ◽  
Cubic Polynomial ◽  
Temperature And Pressure ◽  
Fitting Parameters

Abstract The relationships among the pressure P, volume V, and temperature T of solid-state materials are described by their equations of state (EOSs), which are often derived from the consideration of the finite-strain energy or the interatomic potential. These EOSs consist of typically three parameters to determine from experimental P-V-T data by fitting analyses. In the empirical approach to EOSs, one either refines such fitting parameters or improves the mathematical functions to better simulate the experimental data. Despite over seven decades of studies on EOSs, none has been found to be accurate for all types of solids over the whole temperature and pressure ranges studied experimentally. Here we show that the simple empirical EOS, P = α 1 (PV) + α 2 (PV) 2  + α 3 (PV) 3 , in which the pressure P is indirectly related to the volume V through a cubic polynomial of the energy term PV with three fitting parameters α 1 –α 3 , provides accurate descriptions for the P-vs-V data of condensed matter in a wide region of pressure studied experimentally even in the presence of phase transitions.

The Consequences of Extensivity

2019 ◽  
pp. 159-164
Author(s):  
Robert H. Swendsen
Keyword(s):  
Euler Equation ◽  
Chemical Potential ◽  
Equations Of State ◽  
Fundamental Equation ◽  
Duhem Equation ◽  
Thermodynamic Potentials ◽  
Temperature And Pressure

While not all thermodynamic systems are extensive, those that are homogeneous satisfy the useful postulate of extensivity. In this chapter we return to the thermodynamic postulates and consider the consequences of extensivity. The Euler equation can be derived from extensivity, and the Gibbs–Duhem equation can be derived from the Euler equation. The Gibbs–Duhem equation shows that changes in the chemical potential are not arbitrary, but are determined by changes in the temperature and pressure for. That in turn simplifies the reconstruction of the fundamental equation from the equations of state. The Euler equation also allows the various thermodynamic potentials to be rewritten in terms of other functions.

A NEW SIMPLE CORRELATION FOR CALCULATING SOLUBILITY OF DRUGS IN SUPERCRITICAL CARBON DIOXIDE

2013 ◽  
Vol 12 (07) ◽  
pp. 1350062 ◽  
Author(s):  
ALI ZEINOLABEDINI HEZAVE ◽  
MOSTAFA LASHKARBOLOOKI
Keyword(s):  
Carbon Dioxide ◽  
Supercritical Carbon Dioxide ◽  
Equations Of State ◽  
Mixing Rules ◽  
Simple Correlation ◽  
The Past ◽  
Different Temperatures ◽  
Temperature And Pressure ◽  
Fitting Parameters ◽  
Supercritical Carbon

During the past 20 years, supercritical fluid (SCF) based technologies have been gaining an increasing attention through the academic and industrial communities due to its advantages. One of the most important parameter for any supercritical-based technologies is the knowledge of the solute solubility at different pressures and temperatures. But, due to several concerns e.g. time and expense, measuring the solubility of all compounds in wide ranges of temperature and pressure is not possible. Respect to this, a new empirical correlation with four fitting parameters has been proposed to correlate the solubility of pharmaceuticals in different temperatures and pressures. The obtained results compared with four widely used density based correlations including Mendez-Santiago and Teja (MST), Bartle et al., Chrastil, Kumar and Johnston (KJ) revealed rather good capability of the proposed simple correlation for predicting the solubility of solutes in supercritical carbon dioxide (SC- CO 2). At last, the obtained results compared with the results of three Equations of State (EoS's) with three different mixing rules.

scholarly journals Modeling of pure components high pressures densities using CK-SAFT and PC-SAFT equations

2018 ◽  
Vol 83 (3) ◽  
pp. 331-343
Author(s):  
Jovana Ilic-Pajic ◽  
Mirko Stijepovic ◽  
Gorica Ivanis ◽  
Ivona Radovic ◽  
Jasna Stajic-Trosic ◽  
...  
Keyword(s):  
High Pressures ◽  
Equations Of State ◽  
Model Parameters ◽  
Calculated Density ◽  
Average Percentage ◽  
Pure Compounds ◽  
Density Values ◽  
Temperature And Pressure ◽  
Good Agreement

SAFT equations of state have been widely used for the determination of different thermo-physical and phase equilibria properties. In order to use these equations as predictive models it is necessary to calculate the model parameters. In this work CK-SAFT and PC-SAFT equations of state were applied for the correlation of pure compounds densities in the wide ranges of temperature and pressure (288.15?413.15 K and 0.1?60 MPa, respectively). The calculations of densities for n-hexane, n-heptane, n-octane, toluene, dichloromethane and ethanol, under high pressure conditions, were performed with the new sets of parameters determined in this paper by CK-SAFT and PC-SAFT. Very good agreement between experimental and calculated density values was achieved, having absolute average percentage deviations lower than 0.5 %.

scholarly journals Joule-Thomson coefficients and inversion curves from newly developed cubic equations of state

2019 ◽  
Vol 10 (3) ◽  
pp. 244-255
Author(s):  
Binay Prakash Akhouri ◽  
Sumit Kaur
Keyword(s):  
Carbon Dioxide ◽  
Constant Pressure ◽  
Equations Of State ◽  
Accurate Prediction ◽  
Temperature And Pressure ◽  
And Inversion ◽  
Made In

In this work, we have generalized different parametric forms of cubic equations of state (EoSs) to predict complete Joule-Thomson (J-T) inversion curves for methane at wide temperature and pressure ranges. EoSs of the Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), Patel-Teja (PT), Esmaeilzadeh-Roshanfekr (ER) and the Hagtalab-Kamali-Mazloumi-Mahmoodi (HKMM) along with frequently used cohesion functions α(Tr) have been considered for plot of J-T inversion curves. The PR EoS along with different cohesion functions such as those of the Soave, Antonin Chapoy and the Tau-Sim-Tassone have been also tested for accurate prediction of the inversion curves. The four parametric EoSs of Adachi-Lu-Sugie (ALS), and Lawal-Lake-Silberberg (LLS) with their associated cohesion functions have been used for the prediction of J-T inversion curves. It has been observed that for the plot of inversion curves the LLS EoS is inadequate while the ER EoS agrees well with the previous measurements made in Laboratory. Besides, the J-T coefficient measurements from EoSs have been made for carbon dioxide and nitrogen gases at temperatures from 273.15 to 473.15 K and at pressures from 10 to 1000 atm, respectively. The uncertainties of experimental J-T coefficients data of carbon dioxide from values calculated using EoSs at constant pressure of 1 atm and 20 atm and with varying temperatures have been studied.

scholarly journals Сollapse of weakly-nonspherical cavitation bubble in acetone and tetradecane

2018 ◽  
Vol 13 (3) ◽  
pp. 23-28 ◽  
Author(s):  
D.Yu. Toporkov
Keyword(s):  
Shock Wave ◽  
Mass Transfer ◽  
Cavitation Bubble ◽  
Thermal Conduction ◽  
Equations Of State ◽  
Bubble Radius ◽  
Bubble Surface ◽  
Converging Shock Waves ◽  
Wide Range ◽  
Temperature And Pressure

Collapse of a weakly-spherical cavitation bubble in acetone and tetradecane is studied. The bubble radius is 500 μm, the temperature and pressure of the liquid are 293 K and 15 bar in the case of acetone and 663 K and 50 bar in the case of tetradecane. A hydrodynamic model is used in which the compressibility of the liquid, the nonstationary thermal conduction of the vapor and the liquid, and nonequilibrium heat and mass transfer on the bubble surface, as well as imperfection of the vapor, are considered. Realistic wide-range equations of state are used. It has been found that converging shock waves appear in the bubbles during its collapses in acetone and tetradecane. The maximum values of the thermodynamic parameters are comparable. A comparison of the evolution of the bubble sphericity perturbation and motion of the shock wave in the bubble allows suggesting that tetradecane is a more favorable medium for the realization of a near-spherical cumulation in a bubble than acetone.

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