Wdom B 1965 Equation of state near the critical point J. Chem. Phys. 43 3898 Neece G A and Wdom B 1969 Theories of liquids Ann. Rev. Phys. Chem. 20 167 [Pg.556]

The EOSs are mainly used at higher pressures or when some of the components are near or above their critical point. The most commonly used cubic equations of state are the Peng-Robinson [3] and the Soave-Redlich-Kwong [4] equations. [Pg.424]

Widom B 1965 Equation of state near the critical point J, Chem. Phys. 43 3898 [Pg.556]

The Peng-Robinson equation is related to the R-K-S equation of state and was developed to overcome the instability in the R-K-S equation near the critical point see Peng and Robinson (1976). [Pg.463]

The equation of state is valid from the triple point to 500 K with pressures to 100 MPa. At higher pressures, the deviations from the equation increase rapidly, and it is not recommended to use the equation above 100 MPa. The uncertainties in the equation are 0.3% in density (approaching 1% near the critical point), 0.2% in vapor pressure, and 2% in heat capacities. For viscosity, estimated uncertainty is 2%. For thermal conductivity, estimated uncertainty, except near the critical region, is 4-6%. [Pg.243]

P4.21 (a) The Dieterici equation of state is purported to have good accuracy near the critical point. It does fail [Pg.87]

The above derivation leads to an equation for y in terms of (Sp / dz). Van der Waals paper also contains a variety of other items, such as stability considerations, the pressure in the interfacial layer, spherical interfaces, the value of y near the critical point, a discussion on the thickness of the transition layer, the effect of higher terms in the series expansion of the profile and corresponding state features. Van der Waals also showed that his theory agreed with Gibbs adsorption law, an issue that was later discussed in more detail by Widom J. In the present context we shall not discuss these features further, except to mention that for the temperature dependence close to the critical point T van der Waals predicted [Pg.150]

The results of Amagat s and Raveau s work may be summed up in the statement that, whereas the theorem of corresponding states holds good very approximately, the equation of van der Waals gives results quite inconsistent with the experimental values, especially near the critical point. [Pg.238]

The equation of state determined by Z (A, V, T ) is not known in the sense that it carmot be written down as a simple expression. However, the critical parameters depend on s and a, and a test of the law of corresponding states is to use the reduced variables T, and as the scaled variables in the equation of state. Figure A2.3.5 b) illustrates this for the liquid-gas coexistence curves of several substances. As first shown by Guggenheim [19], the curvature near the critical point is consistent with a critical exponent P closer to 1/3 rather than the 1/2 predicted by van der Waals equation. This provides additional evidence that the law of corresponding states obeyed is not the form associated with van der Waals equation. Figure A2.3 5 (b) shows that P/pkT is approximately the same function of the reduced variables and R [Pg.463]

Figure 3. The minimum value of F along the critical Figure 4. Schematic representation of the p — T plan isotherm calculated from various equations of state, near the critical point in terms of the parametric |

In both equations, k and k are proportionality constants and 0 is a constant known as the critical exponent. Experimental measurements have shown that 0 has the same value for both equations and for all gases. Analytic8 equations of state, such as the Van der Waals equation, predict that 0 should have a value of i. Careful experimental measurement, however, gives a value of 0 = 0.32 0.01.h Thus, near the critical point, p or Vm varies more nearly as the cube root of temperature than as the square root predicted from classical equations of state. [Pg.395]

First-principle calculations of the thermodynamic properties are more or less hopeless enterprise. One of the most famous phenomenological approaches was suggested by van der Waals [6, 8, 9]. Using the dimensionless pressure tt = p/pc, the density 1/ = n/ric and the temperature r = T/T, the equation of state for the ideal gas reads tt = Sot/ 3 — i/) — 3u. Its r.h.s. as a function of the parameter u has no singularities near 0=1 1/ = n = t = is the critical point) and could be expanded into a series in the small parameter T] = n — 71c)/t7c with temperature-dependent coefficients. Solving this [Pg.7]

Before preceding, it is useful to consider the form of the force-force correlation function, which is given in Equation (21), with Equations (22), (24), (25), (26) and (27). The form of the force-force correlation function, derived using density functional formalism, is employed because it permits the use of very accurate equations of state for solvents like ethane and CO2 to describe the density dependence and temperature dependence of the solvent properties. These equations of state hold near the critical point as well as away from it. Using the formalism presented above, we are able to build the known density and temperature-dependent properties of the [Pg.659]

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