Written

To predict vapor-liquid or liquid-liquid equilibria in multicomponent systems, we require a method for calculating the fugacity of a component i in a liquid mixture. At system temperature T and system pressure P, this fugacity is written as a product of three terms... 

The computer subroutines for calculation of vapor-phase and liquid-phase fugacity (activity) coefficients, reference fugac-ities, and molar enthalpies, as well as vapor-liquid and liquid-liquid equilibrium ratios, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements and CDC 6400 execution times for these subroutines are given in Appendix J. 

These subroutines are capable of treating multicomponent systems with up to 20 components. For compatibility with diverse, user-written main programs, they employ vectors of length N, where N ( 20) is the number of components involved, in their argument lists. 

The subroutines PARIN and PARCH are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and should be compatible with most computer systems where input can be taken from logical unit 3. 

The programs DRFLA for vapor-liquid and DRELI for liquid-liquid calculations are written in FORTRAN IV source language for the CDC 6400 of the Computer Center, University of California, Berkeley. Minor modifications, mostly with regard to input and output, will be required for implementation on most other computer systems. 

Consider the single-stage phase split shown in Fig. 3.1a. Overall material balances and component material balances can be written as... 

To calculate the vapor load for a single column of a sequence, start by assuming a feed condition such that q can be fixed. Initially assume saturated liquid feed (i.e., q = 1). Equation (5.1) can be written for all NC components of the feed and solved for the necessary values of 0. There are (JVC - 1) real positive values of 0 which satisfy Eq. (5.1), and each lies between the a values of the... 

Equation (5.3) can be written at minimum reflux and then at finite reflux, say, 1.1 times minimum reflux. The calculation is then repeated for all columns in the sequence. 

Because only light key and lighter components go to the distillate and heavy key and heavier components go to the bottoms, Eq. (5.7) can be written in terms of the molar flow rate of each component in the feed ... 

Beer s law This states that the proportion of light absorbed depends on the thickness d) of the absorbing layer, and on the molecular concentration (c) of the absorbing substance in the layer. It is an extension of Lambert s law, and may be written in the form... 

Dieterici s equation A modification of van der Waals equation, in which account is taken of the pressure gradient at the boundary of the gas. It is written... 

Eigen function In wave mechanics, the Schrodinger equation may be written using the Hamiltonian operator H as... 

Carbon atom 1 in this formula is asymmetric and two stereoisomers therefore exist, depending on whether the OH group is written below (a) or above ( ) the plane of carbon atoms. Both forms crystallize either as the monohydrate or anhydrous. 

When the formulae of other sugars are written in this way those which have the configuration... 

The prefix is also used in orthophosphates, orthocarbonates, orthoformates and ortho-silicates, which are derivatives of POCOH), the hypothetical C(OH)4, HC(OH)3 and Si(OH)4 respectively in these the word ortho is always written in full. 

OH groups are in the para or 1,4 position to each other. This use of the prefix is confined to disubstituted benzene derivatives in such cases as para-hydrogen and paraldehyde the prefix has no uniform structural significance and is always written in full. 

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These methods can be written into standards such as the following ... 

The specific heat for a liquid at constant pressure, written as and expressed in kJ/(kg-K), can be calculated for mixtures in two ways ... 

Thermal conductivity is expressed in W/(m K) and measures the ease in which heat is transmitted through a thin layer of material. Conductivity of liquids, written as A, decreases in an essentially linear manner between the triple point and the boiling point temperatures. Beyond a reduced temperature of 0.8, the relationship is not at all linear. For estimation of conductivity we will distinguish two cases < )... 

The determination of equilibria is done theoretically via the calculation of free energies. In practice, the concept of fugacity is used for which the unit of measurement is the bar. The equation linking the fugacity to the free energy is written as follows >... 

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