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.

The solid-fluid equilibrium of helium above 5000 atm. pressure

1951 ◽  
Vol 207 (1089) ◽  
pp. 268-277 ◽  
Keyword(s):  
Critical Temperature ◽  
Critical Point ◽  
Boiling Point ◽  
Melting Curve ◽  
Complete Agreement ◽  
Suitable Model ◽  
Melting Curves ◽  
Model Substance ◽  
Other Substances ◽  
Semi Empirical

The melting curves of helium and other low boiling-point substances as determined in the laboratory might be expected to imitate those of other substances at much higher, and unattainable, pressures. This was suggested by Simon, who with Ruhemann and Edwards later determined the melting curves of several low boiling-point substances up to about 5000 atm. pressure. There was no suggestion of any solid-fluid critical point, although the temperature reached in the case of helium was eight times the liquid-vapour critical temperature. In spite of anomalous behaviour at lower temperatures, helium is the most suitable model substance for this study, and the melting curve of helium has now been followed still further, up to about 50° K and 7500 atm., with no suggestion of a critical point. Several improvements in technique have been introduced in the present investigation; the results obtained are in complete agreement with the semi-empirical formula originally proposed by Simon, Ruhemann & Edwards.

On physical adsorption XVII. Experimental verification of the two-dimensional van der Waals equation of state above and below the critical temperature

1962 ◽  
Vol 265 (1323) ◽  
pp. 455-462 ◽  
Keyword(s):  
Critical Temperature ◽  
Carbon Tetrachloride ◽  
Equation Of State ◽  
Adsorption Isotherms ◽  
Physical Adsorption ◽  
Van Der Waals ◽  
Phase Changes ◽  
Two Dimensional ◽  
Van Der Waals Equation ◽  
Surface Field

Adsorption isotherms of carbon tetrachloride, chloroform and fiuorotrichloromethane on a substrate of graphitized carbon are reported at temperatures between 200 and 300 °K. Evidence is presented that at these temperatures the residual heterogeneity of the substrate is not observed: under these conditions the true equation of state of the adsorbed film can be deduced directly from the measured adsorption isotherms. All the data reported are described by the adsorption isotherm equation corresponding to a two-dimensional van der Waals gas; this description continues to apply at temperatures where the isotherms show discontinuities characteristic of first-order phase changes. The two-dimensional critical temperature of each of the adsorbed films is rather less than the value predicted by the two dimensional van der Waals equation; this is taken as evidence for the polarization of the adsorbate molecules by an electric field present at the graphite surface. The results obtained with the isotropic carbon tetrachloride molecule indicate a surface field of 1 x 10 5 e. s. u./cm 2 ; we deduce that the anisotropic adsorbates should be oriented at the interface, with the axis of the permanent dipole alined with the surface field.

Simple Pressure and Energy State Equations for Lennard-Jones (12,6) Fluid

1990 ◽  
Vol 112 (1) ◽  
pp. 240-244 ◽  
Author(s):  
H. M. Paynter ◽  
E. P. Fahrenthold ◽  
G. Y. Masada
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Energy State ◽  
Van Der Waals ◽  
Saturation Curve ◽  
State Equations ◽  
Configurational Energy ◽  
Van Der Waals Equation ◽  
Lennard Jones ◽  
Direct Extension

A recently published (Paynter, 1985, 1988) simple veridical equation of state represents a direct extension and generalization of the classical van der Waals equation, yet at the same time remains consistent with modern nonanalytical expansions about the critical point. With the use of this particular equation of state, compact expressions are here obtained for the pressure and configurational energy of the Lennard-Jones (12, 6) fluid, together with a saturation curve and other coexistence properties.

PVT MEASUREMENTS IN THE CRITICAL REGION OF XENON

1954 ◽  
Vol 32 (2) ◽  
pp. 98-112 ◽  
Author(s):  
H. W. Habgood ◽  
W. G. Schneider
Keyword(s):  
Critical Temperature ◽  
Critical Point ◽  
Critical Region ◽  
Critical Pressure ◽  
Critical Density ◽  
Van Der Waals Equation ◽  
The Third ◽  
Critical Isotherm ◽  
Pvt Measurements ◽  
Derivatives Of

Extensive PVT measurements of xenon extending from 1.8° above the critical temperature to the critical temperature, and in a few cases to 4 ° below the critical temperature, have been carried out at densities ranging from somewhat above the critical density to well below. In order to make the corrections for hydrostatic head small and easily calculable, a bomb having a height of only 1.0 cm. was used in the present measurements. The previously reported value for the critical temperature 16.590° is confirmed. The critical density is estimated to be 1.099 ± 0.002 gm./ml. compared with 1.105 gm./ml. found previously. The critical pressure is found to be 57.636 ± 0.005 atm.The isotherms at temperatures above the temperatures of meniscus disappearance do not appear to have any flat portions. However, the critical isotherm is considerably flatter and broader over a range of densities than that corresponding to a van der Waals equation, and at the critical point the third and fourth derivatives of pressure with respect to volume appear to be zero.

scholarly journals Local Shape of the Vapor–Liquid Critical Point on the Thermodynamic Surface and the van der Waals Equation of State

2021 ◽  
Vol 9 ◽  
Author(s):  
J. S. Yu ◽  
X. Zhou ◽  
J. F. Chen ◽  
W. K. Du ◽  
X. Wang ◽  
...  
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Van Der Waals ◽  
Usual Condition ◽  
Local Shape ◽  
Van Der Waals Equation ◽  
Usual Form ◽  
Zero Gaussian Curvature ◽  
Two Parameters ◽  
Vapor Liquid

Differential geometry is a powerful tool to analyze the vapor–liquid critical point on the surface of the thermodynamic equation of state. The existence of usual condition of the critical point (∂p/∂V)T=0 requires the isothermal process, but the universality of the critical point is its independence of whatever process is taken, and so we can assume (∂p/∂T)V=0. The distinction between the critical point and other points on the surface leads us to further assume that the critical point is geometrically represented by zero Gaussian curvature. A slight extension of the van der Waals equation of state is to letting the two parameters a and b in it vary with temperature, which then satisfies both assumptions and reproduces its usual form when the temperature is approximately the critical one.

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.

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