Critical Properties of Isobaric Processes of Lennard-Jones Gases

2005 ◽  
Vol 60 (1-2) ◽  
pp. 23-28
Author(s):  
Akira Matsumoto
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Gibbs Free Energy ◽  
Canonical Ensemble ◽  
Thermodynamic Quantities ◽  
Lennard Jones ◽  
The Laplace Transform ◽  
Enthalpy And Entropy

The thermodynamic quantities of Lennard-Jones gases, evaluated till the fourth virial coefficient, are investigated for an isobaric process. A partition function in the T-P grand canonical ensemble Y(T,P,N) may be defined by the Laplace transform of the partition function Z(T,V,N) in the canonical ensemble. The Gibbs free energy is related with Y(T,P,N) by the Legendre transformation G(T,P,N) = −kT logY(T,P,N). The volume, enthalpy, entropy, and heat capacity are analytically expressed as functions of the intensive variables temperature and pressure. Some critical thermodynamic quantities for Xe are calculated and drawn. At the critical point the heat capacity diverges to infinity, while the Gibbs free energy, volume, enthalpy, and entropy are continuous. This suggests that a second-order phase transition may occur at the critical point.

First and Second-Phase Transitions of Gases at Isobaric Process; Lennard–Jones (9,6) Gases with a Hard Core

2014 ◽  
Vol 69 (12) ◽  
pp. 665-672
Author(s):  
Akira Matsumoto
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Free Energy ◽  
Critical Point ◽  
Thermodynamic Functions ◽  
Order Phase Transition ◽  
Boiling Point ◽  
Hard Core ◽  
Lennard Jones ◽  
Isobaric Process

AbstractThe thermodynamic functions for Lennard-Jones (9,6) gases with a hard core that are evaluated till the third virial coefficients, are investigated at an isobaric process. Some thermodynamic functions are analytically expressed as functions of intensive variables, temperature, and pressure. Some thermodynamic quantities for carbon dioxide are calculated numerically and drawn graphically. In critical states, the heat capacity diverges to infinity at the critical point while the Gibbs free energy, volume, enthalpy, and entropy are continuous at the critical point. In the coexistence of two phases, the boiling temperatures and the enthalpy changes of vaporization are obtained by numerical calculations for 20 substances. The Gibbs free energy indicates a polygonal line; entropy, volume, and enthalpy jump from the liquid to gaseous phase at the boiling point. The heat capacity does not diverge to infinity but shows a finite discrepancy at boiling point. This suggests that a first-order phase transition at the boiling point and a second-order phase transition may occur at the critical point.

Thermodynamic Quantities of Square-Well Gases at Isobaric Process

2010 ◽  
Vol 65 (6-7) ◽  
pp. 561-567 ◽  
Author(s):  
Akira Matsumoto
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Free Energy ◽  
Critical Point ◽  
Thermodynamic Functions ◽  
Order Phase Transition ◽  
Boiling Point ◽  
Thermodynamic Quantities ◽  
Square Well ◽  
Isobaric Process

The thermodynamic functions for square-well gases evaluated till the third virial coefficient are investigated at an isobaric process. Some thermodynamic functions are analytically expressed as functions of intensive variables, temperature, and pressure. Some thermodynamic quantities for H2O are calculated numerically and drawn graphically. In critical states, the heat capacity, thermal expansivity, and isothermal compressibility diverge to infinity at the critical point while the Gibbs free energy, volume, enthalpy, and entropy are continuous at the critical point. In the coexistence of two phases, the boiling temperatures and the enthalpy changes of vaporization are obtained by numerical calculations for 16 substances. The Gibbs free energy indicates a polygonal line; entropy, volume, and enthalpy jump from the liquid to the gaseous phase at the boiling point. The heat capacity does not diverge to infinity but shows a finite discrepancy at boiling point. This suggests that a first-order phase transition at the boiling point and a second-order phase transition at the critical point may occur.

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

scholarly journals THE CRITICAL POINT OF UNORIENTED RANDOM SURFACES WITH A NONEVEN POTENTIAL

1993 ◽  
Vol 08 (06) ◽  
pp. 1139-1152
Author(s):  
M.A. MARTÍN-DELGADO
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Discrete Model ◽  
Recursion Relation ◽  
Scaling Limit ◽  
Random Surfaces ◽  
Matrix Ensemble ◽  
Quartic Interaction ◽  
Double Scaling Limit

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double scaling-limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a quartic interaction.

scholarly journals Rationalisation of the activities of phenolic (vitamin E-type) antioxidants

2003 ◽  
Vol 17 (4) ◽  
pp. 753-762
Author(s):  
Christopher J. Rhodes ◽  
Thuy T. Tran ◽  
Philip Denton ◽  
Harry Morris
Keyword(s):  
Free Energy ◽  
Vitamin E ◽  
Gibbs Free Energy ◽  
State Theory ◽  
Linear Free Energy Relationship ◽  
Free Energies ◽  
Gibbs Free Energy Change ◽  
Linear Free Energy ◽  
Free Energy Of Activation ◽  
Enthalpy And Entropy

Using Transition-State Theory, experimental rate constants, determined over a range of temperatures, for reactions of vitamin E type antioxidants are analysed in terms of their enthalpies and entropies of activation. It is further shown that computational methods may be employed to calculate enthalpies and entropies, and hence Gibbs Free Energies, for the overall reactions. Within the Linear Free Energy Relationship (LFER) assumption, that the Gibbs Free Energy of activation is proportional to the overall Gibbs Free Energy change for the reaction, it is possible to rationalise, and even to predict, the relative contributions of enthalpy and entropy for reactions of interest, involving potential antioxidants.

Thermodynamics of The Pd43Ni10Cu27P20 Bulk Metallic Glass Forming Alloy

2003 ◽  
Vol 806 ◽  
Author(s):  
Masahiro Kuno ◽  
Ludi A. Shadowspeaker ◽  
Jan Schroers ◽  
Ralf Busch
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Metallic Glass ◽  
Specific Heat ◽  
Bulk Metallic Glass ◽  
Gibbs Free Energy ◽  
Specific Heat Capacity ◽  
Undercooled Liquid ◽  
Glass Forming ◽  
Crystalline Mixture

ABSTRACTThe thermodynamics of the bulk metallic glass forming Pd43Ni10Cu27P20 alloy were investigated with differential scanning calorimetry (DSC). The specific heat capacity of the undercooled liquid with respect to the crystalline mixture was measured in the DSC simultaneously with the enthalpy of crystallization over the entire supercooled liquid region. The enthalpy, entropy, and Gibbs free energy change between the liquid and the crystalline mixture was determined from the specific heat capacity data. The calculated enthalpy function closely matched the enthalpies of crystallization that were measured in the DSC, which verifies the validity of the thermodynamic model used. A small Gibbs free energy difference between undercooled liquid and crystalline mixture was found for decreasing temperature in Pd43Ni10Cu27P20 when compared to other glass forming alloys. This reflects a small driving force for crystallization when undercooling this alloy and is the main contributing factor for its high glass forming ability.

Free energy

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Helmholtz Free Energy ◽  
Chemical Potential ◽  
Free Energies ◽  
Central Concept ◽  
Mathematical Properties ◽  
Closed Systems ◽  
Coupled Reactions ◽  
Enthalpy And Entropy

A critical chapter, explaining how the principles of thermodynamics can be applied to real systems. The central concept is the Gibbs free energy, which is explored in depth, with many examples. Specific topics addressed are: Spontaneous changes in closed systems. Definitions and mathematical properties of Gibbs free energy and Helmholtz free energy. Enthalpy- and entropy-driven reactions. Maximum available work. Coupled reactions, and how to make non-spontaneous changes happen, with examples such as tidying a room, life, and global warming. Standard Gibbs free energies. Mixtures, partial molar quantities and the chemical potential.

Chemical Thermodynamics

2021 ◽  
pp. 344-364
Author(s):  
Christopher O. Oriakhi
Keyword(s):  
Free Energy ◽  
Phase Change ◽  
Equilibrium Constant ◽  
Gibbs Free Energy ◽  
Chemical Thermodynamics ◽  
Laws Of Thermodynamics ◽  
Core Concepts ◽  
Enthalpy And Entropy Changes ◽  
Enthalpy And Entropy ◽  
The Relationship

Chemical Thermodynamics discusses the fundamental laws of thermodynamics along with their relationships to heat, work, enthalpy, entropy, and temperature. Predicting the direction of a spontaneous change and calculating the change in entropy of a reaction are core concepts. The relationship between entropy, free energy and work is covered. The Gibbs free energy is used quantitatively to predict if reactions or processes are going to be exothermic and spontaneous or endothermic under the stated conditions. Also explored are the enthalpy and entropy changes during a phase change. Finally the Gibbs free energy of a chemical reaction is related to its equilibrium constant and the temperature.

The first-order phase transition of melting for molecular crystals by Frost–Kalkwarf vapor- and sublimation-pressure equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Akira Matsumoto
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Thermodynamic Quantities ◽  
First Order ◽  
Boiling Points ◽  
Enthalpy Changes ◽  
Vapor Pressure Equation ◽  
Solid Phases ◽  
The Difference ◽  
First Order Phase

Abstract Thermodynamic quantities in the coexistence of the liquid and the solid phases for Frost–Kalkwarf vapor- and sublimation-pressure equations are investigated at an isobaric process. Gibbs free energy changes in the gaseous and the liquid phases, ΔG GL, has been derived from the Frost–Kalkwarf vapor-pressure equation. Similarly, Gibbs free energy changes in the gaseous and the solid phases, ΔG GS, may be estimated by the Frost–Kalkwarf sublimation-pressure equations which are determined by data of sublimation pressures and temperatures for 24 substances. In coexistence between the liquid and the solid phases, Gibbs free energy changes in the liquid and the solid phases, ΔG LS, may be expressed as the difference of ΔG GL and ΔG GS. The melting temperatures and enthalpy changes of melting are evaluated by numerical calculations for 24 substances. The behaviors of H2O for the neighborhood at the melting and the boiling points are investigated. The Gibbs free energy indicates two polygonal lines. Entropy, volume and enthalpy jump from the solid to the liquid phase at the melting point and from the liquid to the gaseous phase at the boiling point. The heat capacity does not diverge to infinity but shows a finite discrepancy at the melting and the boiling points. This suggests that first-order phase transitions at the melting and the boiling points may occur.

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