Virtual value

Hji virtual value of the partial molar enthalpy, evaluated at the temper-... 

For the case of nonideal solutions, show that the expressions for the enthalpy balances are of the same form as those given by Eqs. (2-33) through (2-37) except for the fact that the ideal solution enthalpies of the pure components hjit Hfi are replaced by their partial molar values, Hyi or the virtual values of their partial molar enthalpies hjit H i see Chap. 14. 

In the expressions for the activity coefficients y , yj and the virtual values of the partial molar enthalpies fy, the mole fractions must have the sum of unity. This condition is satisfied by use of the following expressions for these mole fractions... 

The proposed approximation amounts to neglecting the partial derivatives of the enthalpy departure functions, the Q s, with respect to the component-flow rates. As shown in Chap. 14, Q appears in the definition of the virtual value of the partial molar enthalpy. For example, for any component i in the liquid phase on plate j, the virtual value of the partial molar enthalpy is given by... 

To account for the deviation of an actual mixture from a perfect gas mixture, it has been demonstrated that the virtual values of the partial molar enthalpies H( may be used in lieu of the partial molar enthalpies / , to obtain the correct enthalpy of the mixture,13 that is,... 

Let the virtual values of the enthalpies of component i in the vapor and liquid phases leaving plate j be denoted by Hji and hji9 respectively. Then the enthalpy balance enclosing stage j (j j= 1, N) is given by... 

Use of the virtual values of the partial molar enthalpies makes it unnecessary to compute the partial molar enthalpies in order to compute the correct enthalpy of a mixture. The virtual values of the partial molar enthalpies are defined as... 

Comparison of Eqs. (14-72) and (14-73) establishes the validity of Eq. (14-66). Consequently, the virtual values of the partial molar enthalpies may be employed in the calculation of the correct enthalpy of a mixture even though the virtual values of the partial molar enthalpies are unequal to the partial molar enthalpies. [The relationship between Rk and H, follows immediately from Eqs. (14-65) and (14-70)]. 

The departure function Q (which is needed in the evaluation of the virtual values of the partial molar enthalpies [Eq. (14-65)]) may be evaluated through the use of an equation of state for the mixture. 

In the calculation of 0, . a mixture virial B is calculated using mixing rules described in Chap. 3 of the monograph. If B is substituted into Eqs. (11) and (12), the result is the virtual value of the partial molar enthalpy, ft Rigorous application of the Almost Band Algorithm requires that the derivative of Q be calculated with respect to temperature for use in the convergence procedure. This was not done in the solution of Examples 5-1 and 5-2. 

Rayport, J., Sviokla, J. (1996). Exploiting the virtual value chain. The McKinsey Quarterly, 1, 20-37. 

Virtual value chain The virtual, information-based equivalent of the value chain model where value is created by gathering, selecting, synthesizing, and distributing information. (From Harvard Business Review, Exploiting the Virtual Value Chain, J.F. Rayport and J.J. Sviokla, November-December, 1995)... 

From Rayport, J. F. and Sviokla, J. J., Exploiting the Virtual Value Chain, Harvard Business Review, Novem-ber-December 1995. 

Polymer (XXII) was investigated using the same procedure, and showed features very similar to those observed for the model compound as clearly shown by the comparison of Figures 16a and 16b. Although the polyamide was not soluble in pure methanol, the similarity between the polymer and the model compound behaviors allowed us to determine a virtual value of its specific rotatory power per monomeric unit [w ]4oo =+40... 

---