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.

Thermodynamic Functions at Isobaric Process of van der Waals Gases

2000 ◽  
Vol 55 (11-12) ◽  
pp. 851-855
Author(s):  
Akira Matsumoto
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Critical Point ◽  
Thermodynamic Functions ◽  
Isothermal Compressibility ◽  
Van Der Waals ◽  
Thermal Expansivity ◽  
Van Der Waals Equation ◽  
Reduced Temperature ◽  
Isobaric Process

Abstract The thermodynamic functions for the van der Waals equation are investigated at isobaric process. The Gibbs free energy is expressed as the sum of the Helmholtz free energy and PV, and the volume in this case is described as the implicit function of the cubic equation for V in the van der Waals equation. Furthermore, the Gibbs free energy is given as a function of the reduced temperature, pressure and volume, introducing a reduced equation of state. Volume, enthalpy, entropy, heat capacity, thermal expansivity, and isothermal compressibility are given as functions of the reduced temperature, pressure and volume, respectively. Some thermodynamic quantities are calculated numerically and drawn graphically. The heat capacity, thermal expansivity, and isothermal compressibility diverge to infinity at the critical point. This suggests that a second-order phase transition may occur at the critical point.

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.

scholarly journals Heat Capacity and Thermodynamic Property of Cesium Tetraborate Pentahydrate

2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Kangrui Sun ◽  
Kaiyu Zhao ◽  
Long Li ◽  
Yafei Guo ◽  
Tianlong Deng
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Free Energy ◽  
Water Resources ◽  
Thermodynamic Property ◽  
Thermodynamic Functions ◽  
Molar Heat Capacity ◽  
Salt Lake ◽  
High Concentration ◽  
Thermal Anomalies

In order to recover cesium tetraborate pentahydrate (Cs2O·2B2O3·5H2O) from the high concentration cesium-containing salt lake brines and geothermal water resources, the molar heat capacity of Cs2O·2B2O3·5H2O has been measured with a precision calorimeter at the temperature from 303 to 349 K. It was found that there is no phase transition and thermal anomalies. The molar heat capacity of cesium tetraborate pentahydrate is fitted as Cp,m (J·mol−1·K−1) = 593.85705 + 48.0694[T − (Tmax + Tmin)/2]/(Tmax − Tmin)/2] + 24.86395[(T − (Tmax + Tmin)/2)/(Tmax − Tmin)/2]2 + 0.53077[(T − (Tmax + Tmin)/2)/(Tmax − Tmin)/2]3, and the relevant thermodynamic functions of enthalpy, entropy, and Gibbs free energy of cesium tetraborate pentahydrate are also obtained at intervals of 2 K from 303 to 349 K.

scholarly journals Heat Capacity and Thermodynamic Properties of Cesium Pentaborate Tetrahydrate

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Kangrui Sun ◽  
Panpan Li ◽  
Long Li ◽  
Yafei Guo ◽  
Tianlong Deng
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Free Energy ◽  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Molar Heat Capacity ◽  
Polynomial Equation ◽  
Adiabatic Calorimeter ◽  
Nitrogen Atmosphere ◽  
Thermal Anomalies

This paper reports the molar heat capacities of β-CsB5O8·4H2O, which were measured by an accurate adiabatic calorimeter from 298 to 373 K with a heating rate of 0.1 K/min under nitrogen atmosphere. Neither phase transition nor thermal anomalies were observed. The molar heat capacity against temperature was fitted to a polynomial equation of Cp,m (J·mol−1·K−1) = 618.07702 + 39.52669[T − (Tmax + Tmin)/2]/(Tmax − Tmin)/2] − 3.46888[(T − (Tmax + Tmin)/2)/(Tmax − Tmin)/2]2 + 7.9441[(T − (Tmax+ Tmin)/2)/(Tmax − Tmin)/2]3. The relevant thermodynamic functions of enthalpy (HT − H298.15), entropy (ST − S298.15), and Gibbs free energy (GT − G298.15) of cesium pentaborate tetrahydrate from 298 to 375 K of 5 K intervals are also obtained on the basis of relational expression equations between thermodynamic functions and the molar heat capacity.

The thermodynamics of the divalent metal fluorides. I. Heat capacity of lead tetrafluorostannate, PbSnF4, from 10.3 to 352 K

1988 ◽  
Vol 66 (4) ◽  
pp. 549-552 ◽  
Author(s):  
Jane E. Callanan ◽  
Ron D. Weir ◽  
Edgar F. Westrum Jr.
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Thermodynamic Functions ◽  
Adiabatic Calorimetry ◽  
Temperature Limit ◽  
Divalent Metal ◽  
Ion Conductor ◽  
Metal Fluorides ◽  
Fast Ion Conductor ◽  
Fast Ion

We have measured the heat capacity of the fast ion conductor PbSnF4 at 10.3 < T < 352 K by adiabatic calorimetry. Our results show anomalous values in the Cp,m in the region 300 < T < 352 K. These are associated with the α–β crystallographic transition reported at 353 K. Because the upper temperature limit of our cryostat is around 354 K, it was impossible to follow the phase transition to completion. A more subtle anomaly in the Cp,m was detected between 130 and 160 K. Standard molar thermodynamic functions are presented at selected temperatures from 5 to 350 K.

THE ISOSPIN DEPENDENCE OF THE NUCLEAR PHASE TRANSITION NEAR THE CRITICAL POINT

2010 ◽  
Vol 19 (08n09) ◽  
pp. 1570-1576
Author(s):  
Z. CHEN ◽  
R. WADA ◽  
A. BONASERA ◽  
T. KEUTGEN ◽  
K. HAGEL ◽  
...  
Keyword(s):  
Phase Transition ◽  
Molecular Dynamics ◽  
Free Energy ◽  
Phase Transitions ◽  
Critical Point ◽  
Critical Phenomena ◽  
Critical Points ◽  
Liquid Mixtures ◽  
Nuclear Phase ◽  
Isospin Dependence

The experimental results reveal the isospin dependence of the nuclear phase transition in terms of the Landau Free Energy description of critical phenomena. Near the critical point, different ratios of the neutron to proton concentrations lead to different critical points for the phase transition which is analogous to the phase transitions in He 4- He 3 liquid mixtures. The antisymmetrized molecular dynamics (AMD) and GEMINI models calculations were also performed and the results will be discussed as well.

scholarly journals Free-energy analysis of the nonhysteretic first-order phase transition of Eu2In

2020 ◽  
Vol 102 (13) ◽  
Author(s):  
B. P. Alho ◽  
P. O. Ribeiro ◽  
P. J. von Ranke ◽  
F. Guillou ◽  
Y. Mudryk ◽  
...  
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Order Phase Transition ◽  
Energy Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Free Energy Analysis ◽  
First Order Phase

Epitaxial Free Energy and Stability under Epitaxial Strain

1998 ◽  
Vol 05 (05) ◽  
pp. 983-988 ◽  
Author(s):  
P. M. Marcus
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Order Phase Transition ◽  
Tetragonal Phase ◽  
First Order ◽  
Epitaxial Strain ◽  
First Order Phase Transition ◽  
The Stability ◽  
First Order Phase ◽  
Stability Limits

First-principles ground-state total-energy calculations show that tetragonal crystals generally have two structures at which the energy is a minimum, which are appropriately called tetragonal phases in equilibrium. The calculations also show that a small isotropic two-dimensional (epitaxial) strain in the basal plane of a tetragonal phase produces a first-order phase transition to another tetragonal phase, By defining and calculating a special free energy for the states produced by epitaxial strain, the stability limits of each phase and the occurrence of a first-order phase transition between them are clearly demonstrated. Epitaxially strained states and the epitaxial free energy are calculated for vanadium. The epitaxial free energy as a function of the epitaxial stress for these strained states is shown to be similar to free-energy curves calculated for other first-order phase transitions which have analytic descriptions.

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