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.

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.

Loci of maxima and minima of thermodynamic functions of a simple fluid

1976 ◽  
Vol 54 (12) ◽  
pp. 1282-1291 ◽  
Author(s):  
John Stephenson
Keyword(s):  
Specific Heat ◽  
Thermodynamic Functions ◽  
Speed Of Sound ◽  
Isothermal Compressibility ◽  
Constant Pressure ◽  
Van Der Waals ◽  
Experimental Results ◽  
Van Der Waals Equation ◽  
Simple Fluid ◽  
Fluid Argon

Some elementary properties of loci of extrema of thermodynamic functions are established and discussed in connection with maxima and minima of the constant volume specific heat, CV, the isothermal compressibility, χT, and the constant pressure specific heat, CP, along isotherms, and the extremum properties of the isobaric coefficient of expansion, αP, along isobars. Experimental results for fluid argon are used to construct the required loci of extrema. Van der Waals' equation is applied to obtain loci of extrema for χT, CP, and αP, for the speed of sound W, and for related inflexion loci.

THE BAROMETRIC FORMULA FOR REAL GASES AND ITS APPLICATION NEAR THE CRITICAL POINT

1933 ◽  
Vol 9 (6) ◽  
pp. 637-640 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Molecular Weight ◽  
Critical Temperature ◽  
Temperature Gradient ◽  
Critical Point ◽  
Van Der Waals ◽  
Critical Value ◽  
Uniform Density ◽  
Van Der Waals Equation ◽  
Other Substances ◽  
Separation Of Isotopes

According to the theory of the continuity of liquid and gaseous states, as expressed for instance in van der Waals' equation, pronounced density differences may exist in a short column of fluid maintained, throughout its length, at the critical temperature. The point in the tube at which the density of the contents has decreased a given percentage from the critical value is the higher the larger the ratio of the critical temperature to molecular weight. For substances like neon the variations are so large that a measurable separation of isotopes may be expected at or near the critical point; for other substances the computed results are at least of the magnitude found by experiment. Also, according to the theory, in order to obtain, at or near the critical point, a column of gas of uniform density a temperature gradient must be allowed to exist along the column.

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 The low temperature heat capacity of Li2Mo0.05W0.95O4

2021 ◽  
Vol 2119 (1) ◽  
pp. 012137
Author(s):  
A E Musikhin ◽  
M A Bespyatov ◽  
T M Kuzin ◽  
V D Grigorieva ◽  
V N Shlegel
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Low Temperature ◽  
Thermodynamic Functions ◽  
Anomalous Behavior ◽  
Zero Temperature ◽  
Temperature Heat ◽  
Low Temperature Heat Capacity ◽  
Lithium Tungstate ◽  
Heat Capacity Function

Abstract The heat capacity of a lithium tungstate single crystal doped by 5% molybdenum Li2Mo0.05W0.95O4 in the range of 78.5–302.8 K was measured by the adiabatic method. No anomalous behavior of heat capacity was found. The heat capacity function was obtained in the range of 0–303 K by extrapolating to zero temperature and fitting experimental points. Thermodynamic functions of entropy, enthalpy increment and Gibbs free energy at 298.15 K were calculated using the obtained data.

scholarly journals Method for constructing the fundamental equation of state that takes into account the peculiarities of the substance behaviour in a wide vicinity of the critical point

2021 ◽  
Vol 2057 (1) ◽  
pp. 012112
Author(s):  
S V Rykov ◽  
I V Kudryavtseva
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Equation Of State ◽  
Critical Point ◽  
Fundamental Equation ◽  
Virial Coefficients ◽  
Phenomenological Theory ◽  
Phase Region ◽  
Scale Functions ◽  
Fundamental Equation Of State

Abstract On the basis of the phenomenological theory of the critical point and the Benedek hypothesis, an expression for the Helmholtz free energy F with scale functions in the density-temperature variables has been developed. The proposed free energy equation has been tested on the example of constructing the fundamental equation of state of 2,3,3,3-tetrafluoropropene (R1234yf). By comparison with the known experimental data on the equilibrium properties of R1234yf – density and pressure on the phase equilibrium line, p-ρ-T-data in the single-phase region, the second and third virial coefficients, isochoric heat capacity, isobaric heat capacity and the sound velocity – the operating range of the equation of state of R1234yf has been established according to temperature from 220 K to 420 K and pressure up to 20 MPa.

Sign in / Sign up

Export Citation Format

Share Document