State diagrams mass fraction

The exergy flow diagram, Figure 2, shows the results of the exergy balances on the various zones of the system. The reference state of zero exergy was taken as P0=l atm, TQ=528 R, mass fraction water"0.3, mass fraction sodium palmitate=0.7. 

When N = 2, the phase mle becomes F = 4 — n. Since there must be at least one phase (n= 1), the maximum number of phase-mle variables which must be specified to fix the intensive state of the system is three namely, P, T, and one mole (or mass) fraction. All equilibrium states of the system can therefore be represented in three-dimensional P-T-composition space. Within this space, the states of pairs of phases coexisting at equilibrium (F=4 — 2 = 2) define surfaces. A schematic three-dimensional diagram illustrating these surfaces for VLE is shown in Fig. 10.1. 

FIGURE 16.6 State diagram of the sucrose-water system. T is temperature, ij/s mass fraction of sucrose. Tf gives the freezing temperature of water and Ts the solubility of sucrose. Tg is the glass transition temperature and Thom the homogeneous nucleation temperature. 

Key characteristics in liquid/liquid systems are the mutual solubility and the concentration of both liquid phases in the equilibrium state. The previously discussed laws of mixed phase thermodynamics can still be applied. The feasibility of a liquid/liquid extraction depends on the occurrence of a miscibility gap and its width at different temperatures. Figure 2.2-1 shows three exemplary plots of the solubility temperature vs. the mass fraction. The letter z symbolizes mass fractions in any one- or two-phased mixture. The binary mixture formic acid/benzene has an upper critical solubility temperature whereas the mixture di-n-propylamine/water features a lower critical temperature. The third example system nicotine/water shows both a lower and an upper critical temperature. From these diagrams the concentrations of... 

A schematic diagram of a tray is shown in Figure 16-10. The column is operating at steady state. A mass balance will be done for the mass balance envelope indicated by Ae dashed outline. The vapor above the trays is assumed to be well mixed thus, the inlet vapor mole frac V does not depend on the position along the tray, The vapor leaving the balance envelope has not yet had a chance to be mixed and its corrposition is a function of position G. The rising vapor bubbles are assumed to perfectly mix the liquid vertically. Thus, x does not depend upon the vertical position z, but the vapor fraction y does depend on z. The liquid mole frac can be a function of the distance G along the tray measured from the start of the active... 

I Adsorption equilibrium data for the system oxygen/nitrogen/active carbon. Presented in a triangular diagram using mass fractions as the concentration scales i9= — 150°C, p = 1 bar). A, B State points of active carbon loaded with pure oxygen and pure nitrogen, respectively. Curve A.. E.. B Locus of the state points of active carbon loaded with gas mixture. 

A cosolvency effect is characterized by the fact that a mixture of two components B and C is better soluble in a (supercritical) solvent A than each of the pure components B or C alone. As a consequence, even closed homogeneous regions (so-called miscibility windows ) surrounded by heterogeneous states in an isobaric T(it/ (C)) diagram might appear. Here, if/ (C) is the solvent-free or reduced mass fraction of component C defined as u (C) = u (C)/(u (B)-h u>(C)). 

Fig. 3 presents the state diagram of the system PEO-water. It is of an eutectic type exhibiting mixed crystal formation and glass transition phenomena like the system mentioned. The graph of the experimentally determined eutectic enthalpy of transformation versus mass fraction of PEO verifies the eutectic composition. 

Fig. 0.5. State diagram, showing the approximate Tg temperatures as a function of mass fraction, for a gelatinized starch-water system (according to Van den Berg, 1986).

One more effect should be taken into account. Because the miscibility of two species depends on the ratio of their molecular mass, the situation arises where, on the change of the outer conditions, the system remains in a thermodynamically stable state for some fractions of definite molecular mass, while already undergoing the phase separation for other fractions. Although this point has practically not been dealt with in the hterature, its role in the formation of a non-equilibrimn frozen structure should be essential. It means that the state of a system turns out to be dependent on its history. Thus, again, the phase diagram by itself yields a poor indication of the system state within the region of immiscibility bomid by the spinodal or binodal curve. 

The mixing and flow patterns of gravitational dry particulate flows in continuous mixer tubes with helical, Kenics-type [1] static mixer elements have been simulated by the distinct element method (DEM) under steady state conditions. In the particular system the subsequent mixer elements were twisted in opposite direction a mixing element twisted clockwise is followed by an element twisted counter-clockwise and so on. A state diagram that gives a general relationship between the mass flow rate and the solids volume fraction in the mixer tube was determined for various construction parameters. 

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