Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing

1964 ◽  
Vol 86 (2) ◽  
pp. 127-130 ◽  
Author(s):  
Grant M. Wilson
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
Liquid Equilibrium ◽  
Vapor Liquid Equilibrium ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Vapor Liquid

Higher Order Conditional Probabilities and Thermodynamics of Binary Molten Alloys

1997 ◽  
Vol 11 (02n03) ◽  
pp. 93-106 ◽  
Author(s):  
O. Akinlade
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Cluster Model ◽  
Excess Free Energy ◽  
Higher Order ◽  
Thermodynamic Quantities ◽  
Equiatomic Composition ◽  
Conditional Probabilities ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The recently introduced four atom cluster model is used to obtain higher order conditional probabilities that describe the atomic correlations in some molten binary alloys. Although the excess free energy of mixing for all the systems studied are almost symmetrical about the equiatomic composition, most other thermodynamic quantities are not and thus, the study enables us to explain the subtle differences in their physical characteristics required to describe the mechanism of the observed strong heterocoordination in Au–Zn or homocoordination in Cu–Ni within the same framework. More importantly, we obtain all calculated quantities for the whole concentration range thus complimenting experimental evidence.

scholarly journals Theoretical investigations on temperature dependence of thermodynamic properties and concentration fluctuations of In-Tl binary liquid alloys by optimization method

BIBECHANA ◽  
2017 ◽  
Vol 15 ◽  
pp. 11-23
Author(s):  
G K Shrestha ◽  
I S Jha ◽  
B K Singh
Keyword(s):  
Free Energy ◽  
Liquid Alloy ◽  
Entire Range ◽  
Excess Free Energy ◽  
Concentration Fluctuations ◽  
Binary Liquid ◽  
Energy Of Mixing ◽  
Different Temperatures ◽  
Free Energy Of Mixing ◽  
Best Fit

The thermodynamic properties, i.e. free energy of mixing (GM), heat of mixing (HM), entropy of mixing (SM) and activity (ai) of the component i (i , and structural property i.e. concentration fluctuations in long wave-length limit [Scc(0)] of In-Tl binary liquid alloy at a specified temperature have been investigated in the framework of quasi-lattice model on assuming the coupled effect of size ratio and entropic (or energetic) as well as enthalpic effect. These properties of In-Tl liquid alloy at 723 K have been computed theoretically by estimating the best fit value of order energy parameter (W) and size ratio () over the entire range of concentration in order to match their experimental values. The best fit value of  W at 723 K has been used to determine the values of W at different temperatures with the help of temperature derivative of W which are then used for the optimization procedure in order to calculate the corresponding values of excess free energy of mixing, partial excess free energy of mixing and activity of the components involved in the alloy at different temperatures. These parameters have been used to investigate the concentration fluctuations in long wavelength limit {Scc(0)} of In-Tl binary liquid alloy at different temperatures over the entire range of concentration which have been used to predict the various other structural properties like excess stability function (EXS), diffusion coefficient ratio (Dm/Did), short range order parameter (α1) at different temperatures.BIBECHANA 15 (2018) 11-23

The rubidium chloride – sodium chloride phase diagram

1970 ◽  
Vol 48 (22) ◽  
pp. 3483-3486 ◽  
Author(s):  
A. D. Pelton ◽  
S. N. Flengas
Keyword(s):  
Phase Diagram ◽  
Free Energy ◽  
Sodium Chloride ◽  
Excess Entropy ◽  
Excess Free Energy ◽  
Thermochemical Data ◽  
Cooling Curves ◽  
Molar Excess ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The phase diagram of the RbCl–NaCl system has been measured by the method of cooling curves. By combining these data with available thermochemical data for the system, the integral molar excess free energy of mixing at 800 °C has been calculated as ΔGE = −632XRbClXNaCl cal/mole; and the integral molar excess entropy of mixing has been calculated as ΔSE = −0.208XRbClXNaCl cal/°K mole. Estimated precisions are ±50 cal for ΔGE and ±0.05 cal/°K mole for ΔSE at XRbCl = XNaCl = 0.5.

VAPOR–LIQUID EQUILIBRIUM MODELING FOR MIXTURES OF HFC-32 + ISOBUTANE AND HFC-32 + HFO-1234ze(E)

2011 ◽  
Vol 19 (02) ◽  
pp. 93-97 ◽  
Author(s):  
RYO AKASAKA
Keyword(s):  
Free Energy ◽  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Dew Point ◽  
Working Fluid ◽  
Liquid Equilibrium ◽  
Vapor Liquid Equilibrium ◽  
Equilibrium Modeling ◽  
Independent Variables ◽  
Vapor Liquid

Vapor–liquid equilibrium (VLE) have been successfully modeled for the binary mixtures of difluoromethane (HFC-32) + isobutane and difluoromethane + trans-1,3,3,3-tetrafluoropropene (HFO-1234ze(E)). These mixtures are considered as possible replacements for conventional refrigerants far from negligible global warming potential (GWP). A multifluid approach explicit in the Helmholtz free energy forms the basis of the model. The independent variables are the temperature, density, and composition. Accurate published equations of state for pure HFC-32, isobutane, and HFO-1234ze(E) are incorporated to calculate the Helmholtz free energy of each component. Typical uncertainties of bubble- and dew-point pressures calculated using the model are within 2%. Although adjustable parameters of the model are determined only from experimental VLE data, it is highly probable that the model reasonably predicts other thermodynamic properties such as enthalpy and heat capacities. Therefore, the model allows practical design and simulation of refrigeration systems using the mixtures as a working fluid.

Theory of Immiscibility in Mineral Systems

1964 ◽  
Vol 33 (266) ◽  
pp. 1015-1023 ◽  
Author(s):  
Robert F. Mueller
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
Standard Free Energy ◽  
Regular Solutions ◽  
Qualitative Interpretation ◽  
Energy Of Mixing ◽  
Mineral Assemblages ◽  
Free Energy Of Mixing ◽  
The Stability ◽  
End Members

SummaryThe theoretical basis for the stability of binary and quasi-binary solutions is discussed with special emphasis on miscibility relations. Solutions of the distribution equations are presented for the case of two and three coexisting regular solutions and this model is used to illustrate the energetics of miscibility relations. The same principles are then extended to give a qualitative interpretation to sequences of mineral assemblages consisting of pyroxenes, amphiboles, micas, and feldspars. A formulation is presented for the intrinsic stability of a solution, which depends on the presence or absence of an excess free energy of mixing, and the extrinsic stability of a solution, which depends on the standard free energy of the component end members.

Gibb‘s Excess Free Energy of Mixing

1972 ◽  
Vol 251O (1) ◽  
Author(s):  
M. P. Khosla ◽  
B. S. Mahl ◽  
S. L. Chopra ◽  
P. P. Singh
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

Excess free energies of mixing at temperatures below 25°. Isopiestic measurements on the systems H2O-NaCl-Na2SO4 and H2O-NaCl-MgSO4

1971 ◽  
Vol 24 (12) ◽  
pp. 2487 ◽  
Author(s):  
CW Childs ◽  
RF Platford
Keyword(s):  
Free Energy ◽  
Vapour Pressure ◽  
Excess Free Energy ◽  
Pressure Measurements ◽  
Experimental Uncertainty ◽  
Free Energies ◽  
Isopiestic Measurements ◽  
Temperature Range ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

Isopiestic vapour pressure measurements have been made on the systems H2O-NaCl-Na2SO4 and H2O-NaCl-MgSO4 at 15� and 0�. Excess free energies of mixing the aqueous salts hare been calculated for various ionic strengths, and the results have been compared with those previously obtained at 25�. ��� Within experimental uncertainty the excess free energies of mixing of aqueous NaCl with aqueous Na2SO4 are the same at 0�, 15�, and 25�. However, the excess free energy of mixing aqueous NaCl with aqueous MgSO4 shows differences which may be just larger than experimental uncertainty over the same temperature range.

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