Beattie-Bridgman

The Beattie-Bridgman equation, a famous equation of state for real gases, may be written... 

The Benedict-Webb-Rubin equation was derived particularly to describe the behaviour of state of gas systems of relatively low molecular weight. It is, in fact, a perfected Beattie-Bridgman equation with 8 individual constants and is usually used in the pressure-explicit form as a function of reciprocal molar volume tr, i.e. 

Partial molar volumes can be expressed by means of the Beattie-Bridgman equation similarly to the case in which virial expansion was used, functional relationships being defined with the use of relation (6.47). Either one of the three approximations defined by relations (6.87) — (6.89) is used for all constants or, as recommended by Beattie et al., the geometrical mean is taken for the constants Aom and c , the Lorentz mean for Bq and the arithmetic mean for a , b , so that... 

For the sake of illustration we have calculated the equilibrium composition of a mixture, formed by decomposition of methane with steam at an initial ratio of 1 2 moles, 900 K and in the 10 to 1000 atm range. Thermochemical data for CH4, H2O, H2, CO will be found in Example 10, for CO2 in Example 11. The calculation was performed according to relations (6.96) — (6.102), constants of the Beattie-Bridgman equation are given in Appendix 11 for the individual pure constituents. The results are plotted in Fig. 24. It will be seen from the plot, that for all constituents 900 K is a high enough temperature for deviations from ideal behaviour to become apparent only at elevated pressure. 

Constants of the Beattie-Bridgman equation are surveyed in Appendix 11. Similarly, Appendix 12 lists constants of the Benedict-Webb-Rubin equation Hirschfelder discusses the posibility of calculating virial coefficients by means of statistical mechanics, including also a list of values published since 1954. 

Generalization of the Beattie-Bridgman equation was suggested by Su and Chang in the form of... 

The Benedict-Webb-Rubin equation may be generalized in a manner similar to that used for the Beattie-Bridgman equation. Modification then leads to... 

Although these relationships are rather complex, the results will not always be proportional in quality to the labour in volved. Much better agreement may be achieved when constants of equations of state are calculated not from generalized relationships, but from values calculated with the aid of known individual constants of suitable reference constituents, similar in structure to the constituent in question. Brown tried to develop this procedure for the Beattie-Bridgman equation. No-... 

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