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Maxwell’s-equal-area-rule

We may discard the last two terms. The reduced coexistence volumes i>/(P) and Vg P) for the liquid and vapor phase are in equilibrium at T < Tc equivalently, so are the corresponding quantities (pi and vapor phases with reference to Fig. 7.1.2 (where, however, the pressure vs. volume is plotted in a highly schematic manner for purely illustrative purposes) we apply Maxwell s equal area rule to require that, for a fixed value of t < 0, V dP = 0 = Vc — l)dP. The last integral follows since... [Pg.399]

Figure A2.3.3 P-V isotherms for van der Waals equation of state. Maxwell s equal areas rule (area ABE = area ECD) determines the volumes of the coexisting phases at subcritical temperatures. Figure A2.3.3 P-V isotherms for van der Waals equation of state. Maxwell s equal areas rule (area ABE = area ECD) determines the volumes of the coexisting phases at subcritical temperatures.
Before turning to the specifics of the PR-EOS, Maxwell s equal-area rule for pure substances will be derived for the van der Waals family of equations and the mathematical structure of these equations will be discussed. Maxwell s equal-area rule, which applies to the subcritical isotherm T < T ), is shown schematically in Fig. 3.6. [Pg.137]

Show that Maxwell s equal-area rule for multicomponent systems takes the... [Pg.289]

This is the well known equal areas rule derived by Maxwell [3], who enthusiastically publicized van der Waal s equation (see figure A2.3.3. The critical exponents for van der Waals equation are t5q)ical mean-field exponents a 0, p = 1/2, y = 1 and 5 = 3. This follows from the assumption, common to van der Waals equation and other mean-field theories, that the critical point is an analytic point about which the free energy and other thermodynamic properties can be expanded in a Taylor series. [Pg.445]

The law of equal areas (Maxwell s rule) which defines the demixtion curve can be expressed as follows [see Appendix L, eqns (L.1) and (L.5)]... [Pg.679]

The function p(v) at fixed temperature (the isotherm) is shown in Fig. 5.1. The curves 1, 2, 3 correspond to different temperatures. The curve 3 corresponds to a temperature above the critical temperature (T > T ). In this state the curve changes smoothly, pressure falls with increase of o, and the substance can be in equilibrium only in the gaseous form. The second curve corresponds to the critical temperature It is the highest temperature at which liquid and vapor states can coexist in balance with each other. At temperature T < Ti (curve 1) the dependence p o) is non-monotonous. To the left of the point B (line AB) the substance is in the mono-phase liquid state, to the right of point G (line GH) the substance is in the mono-phase vapor state. The region between points B and G corresponds to the equilibrium the bi-phase state liquid - vapor. In accordance with the Maxwell s rule, squares of areas BDE and EFG are equal. From the form of isotherms it follows that in pre-critical area (T < Tc) the cubic equation... [Pg.88]

In the region occupied by the polymer chain, solvent molecules are mixed. Let A/ro be the chemical potential of the solvent molecule measured from the value in the pure solvent. From the thermodynamic condition A/xo = (9AF/dNo)n = —(< / )(9 AF/d4>)=0 that the chemical potential of a solvent molecule inside the region occupied by the polymer should be equal to that in the outside region, we can derive Maxwell s rule of equal area for the osmotic pressure in the form... [Pg.23]

Fig. 3. Portion of a thin film chemical potential isotherm, oc -film and -film of different thickness coexist at // = /ie. hmax and hmin are the equilibrium thin film thickness corresponding to pmax and ptnin, respectively. Equality of the two hatched areas follows from Maxwell s rule. Fig. 3. Portion of a thin film chemical potential isotherm, oc -film and -film of different thickness coexist at // = /ie. hmax and hmin are the equilibrium thin film thickness corresponding to pmax and ptnin, respectively. Equality of the two hatched areas follows from Maxwell s rule.

See other pages where Maxwell’s-equal-area-rule is mentioned: [Pg.320]    [Pg.138]    [Pg.15]    [Pg.233]    [Pg.320]    [Pg.138]    [Pg.15]    [Pg.233]    [Pg.53]    [Pg.677]    [Pg.678]   


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