By Biryukov O.N.
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Completely revised and up to date, this new version develops the elemental formalism and theoretical thoughts for learning relativistic box conception at finite temperature and density. It begins with the path-integral illustration of the partition functionality after which proceeds to advance diagrammatic perturbation suggestions.
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II-8(a). The case in which HBE > TSBE at high temperature resulting in the required behavior E E of EB for phase separation. Note that HB−B > 0 and SB−B > 0. 0 µ B E, H BE, and TS BE µ BE TS BE H BE (b) Low temperature No phase separation 0 1 xB Fig. II-8(b). The case in which TSBE > HBE resulting in the behavior of E E for phase separation. Note HB−B > 0, and SB−B > 0. E B which gives no chance 48 Fig. II-9 in xB which diverges to infinity at the critical point. Namely the solution in the super critical region consists of two kinds of clusters; one rich in B and the other in W.
II-85) to (II-87) 49 Taking into account the Gibbs-Duhem relation. eq. (26) and the expression for the chemical potential using the partial pressure, eq. (41), eq. (85) is rewritten as, dp dxB = dpB dxB xB xW − pB pW =0 (II-86) Recall that at a critical point d B /dxB = 0 and hence dpB /dxB = 0. Thus, unless the system is at a critical point, the following relation holds at an azeotrope, xB p = B xW pW (II-87) This occurs quite commonly in aqueous alcohols. As discussed in Chapter III, this situation is problematic in analyzing the vapor pressure data to obtain chemical potentials by the Boissonnas method (1939).
The Boissonnas method, on the other hand, being purely a numerical analysis based on the first principle, the Gibbs-Duhem relation, is free from such a danger. The Boissonnas method, however, starts with the assumption that the most dilute point is in the Henry’s law region. Is this assumption correct? This issue was dealt with by us and it was concluded that the Henry’s law region does not exist even at the mole fraction of a solute as low as 10−5 . , 1998). This still leaves the possibility that Henry’s law is obeyed below 10−5 mole fraction.