A discussion on equations of phase equilibrium between two regular binary phases

1981 ◽  
Vol 46 (6) ◽  
pp. 1433-1438
Author(s):  
Jan Vřešťál
Keyword(s):  
Phase Equilibrium ◽  
Linear Function ◽  
Concentration Dependence ◽  
Absolute Temperature ◽  
Enthalpy Change ◽  
Independent Parameter ◽  
Free Enthalpy ◽  
Regular Solutions ◽  
Regular Model ◽  
Concentration Dependences

The conditions of the existence of extreme on the concentration dependences of absolute temperature (x are mole fractions) T = Tα(xkα) and T = Tβ(xkβ) denoting equilibrium between two binary regular solutions are generally developed under two assumptions: 1) Free enthalpy change of pure components k = i, j at transition from phase α to β is a linear function of temperature. 2) Concentration dependence of excess free enthalpy (identical with enthalpy) of solutions α and β, respectively, is described in regular model by one concentration and temperature independent parameter for each individual phase.

Temperature and concentration dependence of equivalent conductivity in Ca(NO3)2-CaI2-H2O system

1980 ◽  
Vol 45 (6) ◽  
pp. 1639-1645 ◽  
Author(s):  
Jindřich Novák ◽  
Ivo Sláma
Keyword(s):  
Linear Function ◽  
Concentration Dependence ◽  
Mole Fraction ◽  
Constant Temperature ◽  
Salt Concentration ◽  
Free Water ◽  
Water Molecules ◽  
Equivalent Conductivity ◽  
Calcium Salts ◽  
Fraction I

The dependence of the equivalent conductivity on the temperature and composition of the Ca(NO3)2-CaI2-H2O system was studied. The ionic fraction [I-]/([I-] + [NO-3]) was changed from 0.1 to 0.5, the mole fraction of calcium salts (assumed in anhydrous form in the presence of free water molecules) was 0.075-0.200. The equivalent conductivity was found to be a linear function of the ionic fraction at constant temperature and salt concentration.

Chemical Exergy of Fuels and Efficiency Analysis of Energy Utilizations

2017 ◽  
Author(s):  
Zhou Shaoxiang
Keyword(s):  
Heat Balance ◽  
Energy Systems ◽  
Efficiency Analysis ◽  
Enthalpy Change ◽  
Efficiency Evaluation ◽  
Free Enthalpy ◽  
Chemical Potentials ◽  
Chemical Exergy ◽  
Standard Enthalpy Change ◽  
Exergy Balance

Many studies have investigated the chemical exergy of fuels. The results showed that it is equal to the negative standard free enthalpy change (SFEC) of the fuel combustion or the correction value. However, because the products of the combustion still have the chemical potentials of diffusion, the negative SFEC is not the whole of the chemical exergy of fuels. Because the accurate entropy of fuels cannot be obtained, the accuracy of the SFEC is doubtful and some corrections become necessary. But any correction risks misrepresenting the exergy balance of fuel-fired energy systems. In this paper, some important thermodynamic fundamental problems were studied, which showed that the chemical exergy of fuels should be equal to the negative standard enthalpy change. The formulas of total entropy generations and exergy efficiencies of energy utilizations were deduced, so that the exergy efficiency evaluation just needs heat balance data. The case studies were also given.

Modelling of Phase Diagram Boundaries at Equilibrium of Two Binary Regular Phases

1995 ◽  
Vol 60 (6) ◽  
pp. 911-916
Author(s):  
Jan Vřešťál ◽  
Ivo Stloukal
Keyword(s):  
Phase Diagram ◽  
Linear Function ◽  
Regular Solution ◽  
Gibbs Function ◽  
Temperature Dependent ◽  
Regular Solutions ◽  
Liquid Phases ◽  
Simplifying Assumptions ◽  
Two Phases ◽  
Solution Parameter

The conditions of occurrence of extremes on the solidus and liquidus curves in a binary isobaric phase diagram are specified. The solid and liquid phases are regarded as regular solutions in equilibrium. Two simplifying assumptions are made: (i) the Gibbs function of melting of the pure components is a linear function of temperature; (ii) the two phases in equilibrium are regular solutions with a temperature-dependent regular solution parameter. The conditions of occurrence of inflexion points on the solidus and/or liquidus curves are obtained by modelling.

scholarly journals Shear Viscosity of Aqueous Electrolyte Solutions

2019 ◽  
Vol 64 (3) ◽  
pp. 230
Author(s):  
V. M. Makhlaichuk
Keyword(s):  
Concentration Dependence ◽  
Shear Viscosity ◽  
Aqueous Electrolyte ◽  
Electrolyte Solutions ◽  
Main Attention ◽  
Debye Theory ◽  
Aqueous Electrolyte Solutions ◽  
Concentration Dependences ◽  
Dipole Ordering ◽  
Exponential Formula

The kinematic shear viscosity of aqueous electrolyte solutions has been studied. The temperature dependence of this parameter is shown to be described by an exponential formula at T < Td and a formula of the argon-like type at T > Td, where Td is the temperature of the dipole ordering, in the whole considered concentration interval. Main attention is focused on the peculiarities in the temperature and concentration dependences of the shear viscosity in the argon-like interval. It is shown that the root-like concentration dependence can appear, only if the Debye theory of dilute electrolyte solutions is applicable. Beyond its validity domain, the series expansion of the kinematic shear viscosity in the concentration parameter should have an analytical character. The latter behavior is inherent in the concentration dependence of the shear viscosity in the majority of experiments. The error of reproducing the experimental data did not exceed the experimental one, i.e. it was smaller than 4–5%.

scholarly journals Temperature and concentration dependence of viscosity of Mg(NO3)2–H2O systems

1982 ◽  
Vol 60 (23) ◽  
pp. 2883-2888 ◽  
Author(s):  
S. Mahiuddin ◽  
K. Ismail
Keyword(s):  
Temperature Dependence ◽  
Concentration Dependence ◽  
Magnesium Nitrate ◽  
Concentration Dependences ◽  
Isothermal Equation ◽  
Nitrate Solutions

Densities and viscosities of aqueous magnesium nitrate solutions are measured as functions of temperature and composition. The temperature dependence of viscosity is described by the Vogel–Tammann–Fulcher (VTF) equation. By accounting quantitatively for the concentration dependences of all three parameters involved in the VTF equation an improved isothermal equation is obtained, it describes satisfactorily the concentration dependence of viscosity.

scholarly journals A new activity model for Fe–Mg–Al biotites: I—Derivation and calibration of mixing parameters

2021 ◽  
Vol 176 (3) ◽  
Author(s):  
Edgar Dachs ◽  
Artur Benisek
Keyword(s):  
Experimental Data ◽  
Phase Equilibrium ◽  
Dft Calculations ◽  
Density Functional ◽  
Enthalpy Change ◽  
Calorimetric Study ◽  
Phase Equilibrium Data ◽  
Activity Model ◽  
Mixing Parameters ◽  
Equilibrium Data

AbstractA new activity model for Fe–Mg–Al biotites is formulated, which extends that of Mg–Al biotites (Dachs and Benisek, Contrib Mineral Petrol 174:76, 2019) to the K2O–FeO–MgO–Al2O3–SiO2–H2O (KFMASH) system. It has the two composition variables XMg = Mg/(Mg + Fe2+) and octahedral Al, and Fe–Mg and Mg–Al ordering variables resulting in five linearly independent endmembers: annite (Ann, K[Fe]M1[Fe]2M2[Al0.5Si0.5]2T1[Si]2T2O10(OH)2, phlogopite (Phl, K[Mg]M1[Mg]2M2[Al0.5Si0.5]2T1[Si]2T2O10(OH)2, ordered Fe–Mg biotite (Obi, K[Fe]M1[Mg]2M2[Al0.5Si0.5]2T1[Si]2T2O10(OH)2, ordered eastonite (Eas, K[Al]M1[Mg]2M2[Al]2T1[Si]2T2O10(OH)2, and disordered eastonite (Easd, K[Al1/3Mg2/3]M1[Al1/3Mg2/3]2M2[Al]2T1[Si]2T2O10(OH)2. The methods applied to parameterize the mixing properties of the model were: calorimetry, analysis of existing phase-equilibrium data, line-broadening in powder absorption infrared (IR) spectra, and density functional theory (DFT) calculations. For the calorimetric study, various biotite compositions along the annite–phlogopite, annite–siderophyllite (Sid, K[Al]M1[Fe]2M2[Al]2T1[Si]2T2O10(OH)2), and annite–eastonite joins were synthesized hydrothermally at 700 °C, 4 kbar and logfO2 of around − 20.2, close to the redox conditions of the wüstite–magnetite oxygen buffer at that P–T conditions. The samples were characterised by X-ray powder diffraction (XRPD), energy-dispersive scanning electron microprobe analysis, powder absorption IR spectroscopy, and optical microscopy. The samples were studied further using relaxation calorimetry to measure their heat capacities (Cp) at temperatures from 2 to 300 K. The measured Cp/T was then integrated to get the calorimetric (vibrational) entropies of the samples at 298.15 K. These show linear behaviour when plotted as a function of composition for all three binaries. Excess entropies of mixing are thus zero for the important biotite joins. Excess volumes of mixing are also zero within error for the three binaries Phl-Ann, Ann-Sid, and Ann-Eas. KFMASH biotite, therefore, has excess enthalpies which are independent of pressure and temperature (WGij = WHij). A least-squares procedure was applied in the thermodynamic analysis of published experimental data on the Fe–Mg exchange between biotite and olivine, combined with phase-equilibrium data for phlogopite + quartz stability and experimental data for the Al-saturation level of biotite in the assemblage biotite–sillimanite–sanidine–quartz–H2O to constrain enthalpic mixing parameters and to derive enthalpy of formation values for biotite endmembers. For Fe–Mg mixing in biotite, the most important binary, this gave best-fit asymmetric Margules enthalpy parameters of WHAnnPhl = 14.3 ± 3.4 kJ/mol and WHPhlAnn = −8.8 ± 8.0 kJ/mol (3-cation basis). The resulting asymmetric molar excess Gibbs free energy (Gex) departs only slightly from ideality and is negative at Fe-rich and positive at Mg-rich compositions. Near-ideal activity–composition relationships are thus indicated for the Ann–Phl binary. The presently used low value of − 2 kJ/mol for the enthalpy change of the reaction 2/3 Phl + 1/3 Ann = Obi is generally confirmed by DFT calculations that gave − 2 ± 3 kJ/mol for this ∆HFe–Mg order, indicating that Fe–Mg ordering in biotite is weak. The large enthalpy change of ∆HMg-Al disorder = 34.5 kJ/mol for the disordering of Mg and Al on the M sites in Eas (Dachs and Benisek 2019) is reconfirmed by additional DFT calculations. In combination with WHPhlEas = 10 kJ/mol, which is the preferred value of this study describing mixing along the Phl–Eas join, Mg–Al disordering over the M sites of biotite is predicted to be only significant at high temperatures > 1000 °C. In contrast, it plays no role in metamorphic P–T settings.

Residual Gas Reactions in the Electron Microscope: I. Qualitative Observations on the Water Gas Reaction

1968 ◽  
Vol 26 ◽  
pp. 292-293
Author(s):  
Richard E. Hartman ◽  
Roberta S. Hartman ◽  
Peter L. Ramos
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Gas Phase ◽  
Absolute Temperature ◽  
Residual Gas ◽  
Gas Reactions ◽  
Image Position ◽  
The Right ◽  
Water Gas ◽  
Thinning Rate

The action of water and the electron beam on organic specimens in the electron microscope results in the removal of oxidizable material (primarily hydrogen and carbon) by reactions similar to the water gas reaction .which has the form:The energy required to force the reaction to the right is supplied by the interaction of the electron beam with the specimen.The mass of water striking the specimen is given by:where u = gH2O/cm2 sec, PH2O = partial pressure of water in Torr, & T = absolute temperature of the gas phase. If it is assumed that mass is removed from the specimen by a reaction approximated by (1) and that the specimen is uniformly thinned by the reaction, then the thinning rate in A/ min iswhere x = thickness of the specimen in A, t = time in minutes, & E = efficiency (the fraction of the water striking the specimen which reacts with it).

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