P yP ytxtpr[16

where pi is the partial pressure of component i, P the system pressure, and psat the vapour pressure of pure component .

The effect of temperature on ln y is a concern in data correlation; a suitable representation of the temperature effect permits the determination of data for isobaric conditions from data for isothermal conditions, and vice versa. However, a consistency test for isothermal data is much easier than that for isobaric data because the pressure effect is generally much smaller than the temperature effect. The effect of temperature on ln y is related to the partial molar enthalpy. Lu in 1959 considered the variation of excess enthalpies with temperature for binary systems and suggested that the variation of ln y at constant liquid composition be represented by an expression involving three terms for data interpolation and extrapolation:

In the absence of excess enthalpy data, isothermal data determined at three conditions suffice for the

Table 3 Selected acitivity coefficient models

Name

Margules van Laar

Redlich-Kister

Wilson NRTL

Ge/(RT) = xix2 [A + B(xi - x2) + C(xi - x-2)2 + D(xi -x2)3#2]

GE " ! T21G21 T12G12 RT 1 \x1+x2G21 x2#x1G12

where:

Aff12 : RT

Aff21 RT

ln y1 = x2 [B + 2(A - B)x1] ln y2 = xf[A + 2(B - A)x2]

ln j1 =A[1 +Ax1/(Bx2)]-2 ln ^2 = B[1 # Bx2/(Ax1)]-2

ln y1 = a1x;2 + ^1x33 + cx3 + dx4 +2 ln y2 = a2x2 + b2x? + c2x? + d2x4 + ••• where: a1 = A + 3B + 5C + 7D + 2 b1 =- 4(B + 4C + 9D) +2 c1 = 12(C + 5D) +2 d1 "-32D +2 a2 = A - 3B + 5C - 7D +•••

X12G1;

I21 G2

UNIQUAC

GE (combinatorial) $1 $2

RT x1 x2

- q ln (0,i + 6jXj!) + eq e + ejXji ej + eßi where: i= 1, j= 2 or i = 2, j = 1

GE (residual) RT

x1q1

xq1 +x2q2

AU12

21 RT 12 RT

determination of isobaric data within a reasonable range of temperatures. Similarly, if isobaric vapour-liquid equilibrium data are available at three conditions, isothermal data can be obtained by the same approach and then tested for consistency. The number of sets of vapour-liquid equilibrium data required can be reduced when excess enthalpies are available, but generally one set of experimental values should be used in the correlation. In the absence of the required data for the determination of parameters in eqn [17], RT ln y, at a given composition may be assumed to be constant as an approximation. The correlated results can also be used for the prediction purposes.

Equation-of-State Approach

Fugacities of both phases are represented in this approach by the same equation of state, which provides a relationship between the intensive thermodynamic variables T, P, v and composition. Such an equation may be explicit in P or v. The pressure-explicit equations in the form of :

are more useful for solving phase-equilibrium problems. In terms of the fugacity coefficients, ^<V(= fV/yiP) and ^iL(= f,L/x,P), formulation of vapour-liquid equilibria is based on the equilibrium

Table 4 Barker's method for the determination of activity coefficients from experimental data

At equilibrium:

Therefore:

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Solar Panel Basics

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