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 A new formation of diamond

1905 ◽  
Vol 76 (512) ◽  
pp. 458-461 ◽  
Keyword(s):  
Critical Temperature ◽  
Melting Point ◽  
Critical Point ◽  
Boiling Point ◽  
Critical Pressure ◽  
Carbonic Acid ◽  
Melting Points ◽  
Boiling Points ◽  
James Dewar ◽  
New Formation

On the average the critical point of a substance is 1·5 times its absolute boiling-point. Therefore the critical point of carbon should be about 5800° Ab. But the absolute critical temperature divided by the critical pressure is for all the elements so far examined never less than 2·5; this being about the value Sir James Dewar finds for hydrogen. So that, accepting this, we get the maximum critical pressure as follows, viz., 2320 atmospheres:— 5800° Ab./CrP = 2·5, or CrP = 5800° Ab./2·5, or 2320 atmospheres. Carbon and arsenic are the only two elements that have melting-point above the boiling-point; and among compounds carbonic acid and fluoride of silicium are the only other bodies with similar properties. Now the melting-point of arsenic is about 1·2 times its absolute boiling-point. With carbonic acid and fluoride of silicium the melting-points are about 1·1 times their boiling-points. Applying these ratios to carbon we find that its melting-point would be about 4400°.

Diffusion of a solute in dilute solution in a supercritical fluid

1991 ◽  
Vol 433 (1887) ◽  
pp. 63-79 ◽  
Keyword(s):  
Diffusion Coefficient ◽  
Critical Temperature ◽  
Equation Of State ◽  
Supercritical Fluid ◽  
Critical Region ◽  
Critical Density ◽  
Partial Molar Volumes ◽  
Dilute Solution ◽  
Binary Diffusion Coefficient ◽  
Binary Diffusion

The experimental evidence for the behaviour of the binary diffusion coefficient for a solute in dilute solution in a supercritical fluid (a fluid above its critical temperature and pressure) is reviewed. Measurements at very low dilution, particularly by the Taylor dispersion technique, indicate that, at constant temperature a few degrees above the critical temperature, the product of density and the diffusion coefficient exhibits a small, continuous and undramatic variation from zero density to well above the critical density. However, some measurements made at higher, but still very low concentrations (e.g. with mole fractions around 10 -3 ), show a lowering of the coefficient in the critical region. The equations, based on non-equilibrium thermodynamics, are put into a form in which the behaviour of the binary diffusion coefficient in the critical region, but not very close to the critical point, may be examined using an equation of state. Calculations for naphthalene in solution in carbon dioxide are carried out using the van der Waals equation of state for mixtures to indicate the form and order of magnitude of the ‘anomalous’ lowering of the coefficient, and especially its dependence on concentration. These indicate a substantial effect even at naphthalene mole fractions of 4.0 x 10 -4 or less and a temperatures 1, 3 and 9 K above the critical temperature of the pure solvent. In addition the flux of a solute in a supercritical fluid in the critical region with respect to space or cell-fixed coordinates is discussed. Because of the large and negative partial molar volumes of solutes like naphthalene in this region, the frames of reference, according to which the diffusion coefficients are defined, can be caused to move rapidly, commonly towards the source of concentration. Thus fluxes of solute with respect to space-fixed coordinates are further substantially reduced in the critical region. The combination of the lowering of the diffusion coefficient and barycentric motion can therefore cause a very significant reduction of solute mass transfer in the critical region and may be the explanation of the sometimes very large diffusion anomalies observed experimentally.

PERSISTENCE OF THE LIQUID STATE OF AGGREGATION ABOVE THE CRITICAL TEMPERATURE

1938 ◽  
Vol 16b (9) ◽  
pp. 289-302 ◽  
Author(s):  
R. L. McIntosh ◽  
O. Maass
Keyword(s):  
Critical Temperature ◽  
Statistical Mechanics ◽  
Liquid State ◽  
Critical Pressure ◽  
Critical Density ◽  
Small Correction ◽  
Pressure Region ◽  
The Difference ◽  
Liquid States ◽  
Made In

The data obtained by Maass and Geddes (7) on the properties of ethylene in the critical-temperature–critical-pressure region have been substantiated although it was shown that a small correction had to be applied to their absolute values of density. It was shown that at the critical density of ethylene the difference between the densities of the medium below and above the point at which the meniscus disappeared was a maximum. The conclusion of Mayer and Harrison (made in their recent papers on statistical mechanics of condensing systems (6, 10)) that, at a temperature just above that at which the meniscus disappeared, the pressure of the system remains constant over a considerable variation of mass per volume, has been corroborated. The effect of the presence of small measured quantities of air has been examined. The phenomena observed are explained on the basis that there is a difference between the gaseous and liquid states of aggregation with a structure assigned to the latter.

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.

THERMODYNAMIC PROPERTIES OF XENON IN THE CRITICAL REGION

1954 ◽  
Vol 32 (2) ◽  
pp. 164-173 ◽  
Author(s):  
H. W. Habgood ◽  
W. G. Schneider
Keyword(s):  
Critical Temperature ◽  
Thermodynamic Properties ◽  
Critical Region ◽  
High Frequency ◽  
Critical Density ◽  
Preceding Paper ◽  
Acoustic Data ◽  
Dispersion Effects ◽  
Acoustical Data ◽  
Good Agreement

Using the detailed compressibility data in the critical region of xenon given in the preceding paper, supplemented by measurements of Beattie, Barriault, and Brierley over a wider range of temperatures and densities, thermodynamic properties have been calculated for the critical region—extending from the critical temperature to 50° above it and from low densities to somewhat above the critical density. The values of Cυ at the critical density are in good agreement with those calculated from acoustical data at temperatures higher than Tc + 1°; closer to the critical temperature however, the Cυ values derived from the equation of state data become much greater than those derived from the acoustic data. This difference can be accounted for by dispersion effects in the high frequency acoustic data near the critical point.

DENSITY DIFFERENCES AT THE CRITICAL POINT ACCORDING TO R. PLANK'S EQUATION OF STATE

1938 ◽  
Vol 16a (5) ◽  
pp. 89-99 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Critical Temperature ◽  
Equation Of State ◽  
Critical Point ◽  
Relative Difference ◽  
The Third ◽  
Large Correction ◽  
The Difference

If R. Plank's equation of state is assumed to apply, the densities measured at two levels, 1 cm. apart, in a column of gas kept at the critical temperature, may differ by more than 5%. A large correction is therefore required for densities determined at the critical point unless the entire contents of the tube is vigorously stirred. Van der Waal's equation shows that the difference in level corresponding to a relative difference in density, (ρ – ρc)/ρc, is proportional to the third power of the relative difference; according to Wohl's equation it is proportional to the fourth, and according to Plank, to the fifth, power of the relative difference in density.

Strong non-Boussinesq effects near the onset of convection in a fluid near its critical point

2009 ◽  
Vol 642 ◽  
pp. 15-48 ◽  
Author(s):  
GUENTER AHLERS ◽  
BERND DRESSEL ◽  
JAECHUL OH ◽  
WERNER PESCH
Keyword(s):  
Critical Temperature ◽  
Critical Point ◽  
Temperature Difference ◽  
Sulfur Hexafluoride ◽  
Critical Density ◽  
The Other ◽  
Reflection Symmetry ◽  
Linear Temperature ◽  
Other Hand ◽  
Fluid Properties

Measurements of fluctuations and convection patterns in horizontal layers of fluid heated from below and near the onset of Rayleigh–Bénard convection (RBC) are reported under conditions where the fluid properties vary strongly over the temperature range ΔT = Tb − Tt (Tb and Tt are the temperatures at the bottom and top of the sample, respectively). To facilitate a comparison with the data, the theory of Busse (J. Fluid Mech., vol. 30, 1967, p. 625) of these so called non-Oberbeck–Boussinesq (NOB) effects, which applies to the case of relatively weak (and linear) temperature dependences, was extended to arbitrary variations with temperature. It is conceptually useful to divide the variations with temperature of the fluid properties into two disjunct parts. One part is chosen so that it preserves the reflection symmetry of the system about the horizontal midplane, while the remainder breaks that symmetry. The latter, exclusively considered by Busse, leads (in contrast to the formation of the typical convection rolls in RBC) to hexagons immediately above the transition to convection at the critical temperature difference ΔTc. The symmetric part, on the other hand, does not prevent the bifurcation to rolls, but may become very important for the determination of ΔTc. In the experiment the fluid was sulfur hexafluoride at temperatures above but close to the gas–liquid critical point, where all fluid properties vary strongly with temperature. All measurements were done along isobars by varying ΔT. Patterns were observed above onset (ΔT ≳ ΔTc), while for the conduction state at ΔT < ΔTc there were only fluctuations induced by Brownian motion. When the mean temperature Tm = (Tb + Tt)/2 was such that the density ρ at Tm was equal to the critical density ρ*, the mirror symmetry about the horizontal midplane of the sample was essentially preserved. In that case, as expected, we found a direct transition to rolls and the critical temperature difference ΔTc was considerably shifted compared to the critical value ΔTc,OB in the absence of NOB effects. When, on the other hand, Tm was not located on the critical isochore, the NOB effects broke the reflection symmetry and led to a hysteretic transition from fluctuations to hexagonal patterns. In this latter case the hexagonal pattern, the observed hysteresis at onset and the transition from hexagons to rolls at larger ΔT were consistent with the ‘classical’ predictions by Busse.

Investigation in the Vicinity of the Critical Point

1988 ◽  
Vol 43 (8-9) ◽  
pp. 734-740
Author(s):  
I. R. Yukhnovskii
Keyword(s):  
Critical Temperature ◽  
Partition Function ◽  
Critical Point ◽  
Explicit Form ◽  
Reference System ◽  
Chemical Potential ◽  
Critical Density ◽  
Collective Variables ◽  
Potential Surfaces

Abstract It is shown that the events occuring in the vicinity of the critical point can be described in full by means of the collective variables with the appropriate reference system. The partition function containing the explicit form for the quartic measure density is obtained and integrated. Expressions for the critical temperature, critical density and critical chemical potential surfaces are calculated.

MEASUREMENT OF VISCOSITY IN THE CRITICAL REGION. ETHYLENE

1940 ◽  
Vol 18b (5) ◽  
pp. 128-137 ◽  
Author(s):  
S. G. Mason ◽  
O. Maass
Keyword(s):  
Critical Temperature ◽  
Critical Region ◽  
Critical Pressure ◽  
New Method

A precision oscillating disc viscometer has been constructed with a view to studying viscosities of systems at the critical temperature and critical pressure. A new method of computing logarithmic decrements is described and a number of results obtained with ethylene are presented. Of particular interest is the transition in viscosity on an isochore through the critical temperature.

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