Beattie-Bridgeman equation state

Kinetic considerations always lead to an equation of state giving the pressure as a function of the concentration and temperature, but for many purposes it is more convenient to know the molal volume as a function of the pressure and temperature. Beattie1 has indicated how the constants of an equation, similar in form to the Beattie-Bridgeman equation,2 may be obtained from p,V,T data. Often, however, the labor of this determination is not compensated by the added convenience. 

J.A. Beattie O.C. Bridgeman equation of state was first described in ProcAmAcadSci 63, 229(1928), which we did not consult One of the modifications of Beattie Bridgeman equation is given under "Su ... 

Generalized Beattie-Bridgeman Equation of State for Real Gases. It is written by Su Chang as ... 

Su Chang stated that their equation falls into the general form of the Lorentz Equation of State (qv). It may also be regarded as a simplified, generalized form of Beattie-Bridgeman Equation of State (qv)... 

The Beattie-Bridgeman equation, like most equations of state, is explicit in pressure. Certain calculations require an equation that is explicit in volume. Therefore, Beattie rearranged the Beattie-Bridgeman equation and modified it to give the following form. 

While this equation may be considered a modification of the Beattie-Bridgeman equation of state, it is completely empirical. 

A laboratory cell with volume of 0.007769 cu ft contains 0.001944 lb moles of the mixture given in the table below. Temperature is to be raised to 80°F. Calculate the pressure to be expected. Use the Beattie-Bridgeman equation of state. Compare your answers with experimental results of 1200 psia 2%. 

A, B, E coefficients in Beattie modification of Beattie-Bridgeman equation of state... 

The permselectivity for membrane separations can also be calculated by substituting fugacities calculated from an equation of state, here using the Beattie-Bridgeman equation, into Equation (3) for the partial pressure values (4). The values of the permselectivities in Table IV are relatively constant at a fixed feed composition in agreement with the approximately linear behavior noted in Figures 9-11. 

Other semiempirical equations of state can be used to predict Joule-Thomson coefficients. Perhaps the best of these is the Beattie-Bridgeman equation, which can be written (for 1 mol) as... 

Plot the Leimard-Jones potentials for each of the gases studied. Obtain ft from Eqs. (16)-(18) by numerioal integration and compare the values from this two-parameter potential with those from the van der Waals and Beattie-Bridgeman equations of state. Optional A simple square-well potential model can also be used to eradely represent the interaction of two molecules. In place of Eq. (18), use the square-well potential and parameters of Ref. 6 to ealeulate /t. Contrast with the results from the Lennard-Jones potential and comment on the sensitivity of the calculations to the form of the potential.]... 

If the constants in a satisfactory equation of state, e.g., the Beattie-Bridgeman equation, were known, d V/dT )p could be expressed analytically as a function of the pressure, and then integrated in accordance with equation (21.12). The treatment may be illustrated in a simple manner by utilizing the van der Waals... 

Even though a and b are derived from actual P-V-T data, the fugacities obtained from equation (29.14) may not be too reliable over a range of pressures because of the approximate nature of the van der Waals equation. By using a more exact equation of state, such as the Beattie-Bridgeman equation, better values for the fugacities can be obtained, but since this equation involves five empirical constants, in addition to R, the treatment is somewhat more complicated than that given above. ... 

Beattie-Bridgeman Equation. One of the most exact empirical equations of state, useful at high pressures, is that proposed by Beattie and Bridgeman (1928) ... 

Thus, pressure-explicit equations of state for pure substance 1 (for the first integral) and for the gas mixture (the second integral) are required. Five different equations of state have been used in the analysis of this system (1) the five-constant Beattie-Bridgeman equation (2) the eight-constant Benedict-Webb-Rubin equation (3) the twelve-constant modified Martin-Hou equation and (4) and (5), the virial equation using two sets of virial coefficients. The first of these uses pure-substance second and third virial coefficients calculated from the Lennard-Jones 6-12 potential with interaction coefficients determined by the method of Ewald [ ]. The second set differs only in the second virial coefficients and interaction coefficient, these being found using the Kihara potential Solutions of the theoretical equa-... 

The calculation of the volume of a nonideal gas is a root-finding problem. Let us consider, for example, Rice s problem (Rice, 1993) where the Beattie-Bridgeman equation of state joins the temperature T(K), the pressure P(atm), and the molar volume V(l/mol) through the formula... 

Thus, in 1940, Benning and McHamess, on the basis of their experimental pvT data for Freons-11, -21, and -22 T 300-450 K, 0.03-2.1 M.Pa), derived constants for the Beattie-Bridgeman equation of state. For a long time, tables calculated from these equations were presented in reference books [0.7, 0.45, and others]. Table 1 shows that Eq. (0.1) contains only five controllable constants, but the assumption = 0 for freons decreases the power of the equation relative to v to the third. The application range of the Beattie-Bridge-man equation of state is narrow and even at e 7 0 the density stays in the limit (o = 0-0.4 [0.5]. 

Other equations of state can be found in the book by Hirschfelder, Curtiss, and Bird, including the Beattie-Bridgeman equation, with five parameters, and the Benedict-Webb-Rubin equation, with eight parameters. 

Heats of reaction at higher pressures have been calculated by various authors by use of equation of state. Gillespie, Beattie [13] have used the Beattie Bridgeman equation of state, and Kazarnovskii, Karapet yants [27], and Kazar-novskii [26] have used experimental PVT data to calculate the heat of reaction. 

The experimental data at high pressures have been analyzed by different equations of state to calculate the fugacity coefficients in K. Gillespie [11] and Gillespie, Beattie [12] have used the Beattie-Bridgeman equation of state. The method by Newton [44] is a generalized method for calculation of fugacity coefficients. 

The Beattie-Bridgeman equation of state is a specific version of the virial equation ... 

W2) Wobl Equation of State. It is the 4th degree in the volume virial equation proposed in 1914 by Wohl and described in Addnl Ref Aj. it was used by Joffe (Ref 2a) far calcn of parameters of some gases in order to compare the results with those obtd by using the eq (5) of Joffe with equation of Beattie-Bridgeman and vanderWaals Joffe gives (Ref 2a, p 541) for Wohl equation ... 

The early application of volumetric data for hydrocarbons made use of the perfect gas laws. They were not sufficiently descriptive of the actual behavior to permit their widespread use at pressures in excess of several hundred pounds per square inch. The need for accurate metering aroused interest in the volumetric behavior of petroleum and its products at elevated pressures. Table II reviews references relating to the volumetric behavior of a number of components of petroleum and their mixtures. For many purposes the ratio of the actual volume to the volume of a perfect gas at the same pressure and temperature has been considered to be a single-valued function of the reduced pressure and temperature or of the pseudo-reduced (38) pressure and temperature. The proposals of Dodge (15), Lewis (12), and Brown (8) with their coworkers serve as examples of the nature of these correlations. The Beattie-Bridgeman (2) and Benedict (4) equations of state describe the volumetric behavior of many pure substances and their mixtures with an accuracy adequate (31) for most purposes. However, at pressures above 3000 pounds per square inch the accuracy of representation with existing constants leaves something to be desired. 

Beattie-Bridgeman (deton) equation of state 4D271... 

Equations of state (detonation and expin), listing of Abel, Allan, Beattie-Bridgeman, Becker, Becker-Kistiakowsky-Wilson, Benedict-Webb-Rubin, Berthelot, Boltzman, Brinkley-Wilson, Caldirola Paterson, Callendar,... 

This assumption is a good one at present day pressures of 500-800 psia for solids however, proposed operating pressures of 2000-3000 psia even at the temperatures of concern, may require some correction to the perfect gas law. Under these conditions, one should use the Beattie-Bridgeman or van der Waal s equation for the state equation and fugacity coefficients in the equilibrium calculations. 

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