Liquid samples must be introduced into a 10 mm cuvette, which is the reference path length, in order to obtain universal color coordinates. If possible, the spectrum should be recorded with a wavelength resolution of 5 nm as the factors and formulas provided are expressed for this resolution. The blank is measured with distilled water if the sample is liquid or with a blank solid standard if the sample is solid for example, for reflectance analyses commercial standards of CaCO 3 are often used.

Once the transmittance or reflectance spectra of all the samples have been measured, a mathematical treatment is required to obtain the color coordinates.

## Mathematical Modeling with Excel by Brian Albright (2009, Paperback)

Using Template-5nm-for-Students Workbook. In the first sheet, called Template 5 nm , the sample spectrum must be introduced so that all formulas can automatically return the color space coordinates. In addition, some information about this color space and the meaning of its parameters are given. As in the previous sheets, the fourth sheet, called RGB , automatically expresses the obtained R , G , and B values in three graphs: the R graph, the G graph, and the B graph Figure 4 , and the values obtained for each parameter are summarized.

Finally, the sheet called Formulas contains a summary of all equations proposed by the CIE and all formulas used in Microsoft Excel. This sheet was included because teachers may want to introduce some equations to their students, or they may want the students to understand that mathematical treatment of the sample spectrum is not as easy as this spreadsheet file makes it. The file Examples. This file includes four spectra: one spectrum of an orange dye, one of a violet dye, one of a blue dye, and another of a green dye.

Obtained Results with Students.

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These spreadsheet files have been used by chemistry and enology students at our university in order to discuss their experimental results in a laboratory report. Specifically, for chemistry students the color space parameters of different pH indicators phenolphthalein, bromothymol blue, and methyl orange were measured at different pH values. Furthermore, enology students determined the color space coordinates of different wine and alcoholic beverage samples.

The newly developed Microsoft Excel workbooks described here, which not only offer more information on the results but also allow a cell to be colored with an almost identical color to the real sample, have allowed students to understand better and improve their discussion of the results in their laboratory reports. In the first report, the workbook was used in order to better understand the effect of different quantities of polivinylpolipyrrolidone PVPP over the color of red wines. In the second report, the workbook was used in order to describe the color of a wood-aged spirit.

Both reports have been translated from Spanish to English for better comprehension. The files described here were also used in a classroom explanation as a visual and interactive aid. In all cases, the results were satisfactory, and students commented that the sheets provided an easy way to understand color space. In Conclusion. The first Excel sheet was developed so that students can understand the most relevant color spaces, as well as to facilitate the work of teachers when offering explanations for this topic. The second Excel sheet was developed so that researchers working in the laboratory can easily obtain the coordinates of the color spaces most commonly applied in the scientific community.

For this reason, this sheet provides less information that the first sheet, although it can be used to introduce several spectra and thus obtain the color parameters of several samples at the same time. Supporting Information. The authors declare no competing financial interest. The fading rates of some natural dyes. Photofading of wool flannel dyed with madder, fustic, weld, luteolin and apigenin and turmeric curcumin when mordanted with tin or alum was rapid at first and then slowed.

Indigo, cochineal with tin or alum mordant, and fustic with chrome mordant faded at a const. The implication of these findings for museum textiles were discussed. Synthesis of some unsaturated 1,8-naphthalimide dyes.

## Mathematical Modeling with Excel

Dyes Pigm. Four polymerizable derivs. Polyamide fabrics were dyed. Synthesis of some pyridone azo dyes from 1-substituted 2-hydroxypyridone derivatives and their colour assessment. Characterization of the dyes was carried out by spectral and elemental anal. The color parameters of the dyed fabrics were measured. The assessment of color was made in terms of CIE tristimulus values. The correlation between color and structure of the dyes was discussed.

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Ecofriendly ultrasonic natural dyeing of cotton fabric with enzyme pretreatments. Desalination , 1—3 , 62 — 69 , DOI: Elsevier B. Ecofriendly ultrasonic textile dyeing with natural dyes such as Acacia catechu and Tectona grandis show better and faster dye uptake after enzyme pretreatment on cotton fabric, and results of dyeing are better than metal mordanted fabric. It is obsd. The role of enzyme pretreatment is primarily for better absorbency, adherence and dyeability of these dyes on cotton fabric, thereby completely replacing metal mordants with enzyme for adherence of natural dyes on cotton.

SEM show surface characteristics at different stages of dyeing. The effect of sonication on the dyeing is compared with conventional heating. The study also shows enhancement in CIELab values. Elsevier Ltd. CIELAB values were predicted based on a neural network developed for cotton fabric dyed with vinyl sulfone reactive dye.

The neural network developed is a multilayer feed-forward network. To achieve the required depth of color, the CIELAB values of the fabric to be dyed were predicted using trained feed-forward neural network. The results obtained from the network gives an av. The trained network brings out the same error for other dyes as well as for input and output parameters selected beyond the range used for training the network.

## Mathematical Modeling with Excel - CRC Press Book

Neutralisation indicators in 2-methylpropanol: their pKa values and chromatic parameters of transition ranges. Analyst , 2 , — , DOI: A series of com. The dissocn.

The chromaticity coordinates, pKa values, transition pH range, pH of max. A variety of acids and their mixts. Colour specification of pyridinealdehyde and 6-methylpyridinealdehyde p-nitrophenylhydrazones as indicators for pH determination. Talanta , 34 7 , — , DOI: Talanta , 34 7 , ISSN: The physicochemical properties, chromaticity co-ordinates and chromatic parameters for pyridinealdehyde p-nitrophenylhydrazone and 6-methylpyridinealdehyde p-nitrophenylhydrazone proposed as new indicators for calorimetric pH measurements are reported. The sensitivity and rapidity of colour change have been evaluated in terms of specific colour discrimination SCD , pH of maximum colour change and half band-width of change of SCD in terms of pH.

Selection of an optimum pH-indicator for developing lactic acid bacteria-based time-temperature integrators TTI. Food Eng. Among all time-temp. For the development of lactic acid bacteria-based TTIs, optimum pH-indicators were chosen as follows. Five kinds of potential pH-indicators and four species of lactic acid bacteria were used to create microbial-based TTIs. The qualifying stds. In particular, the reaction of TTI color development could be enhanced from non zero-order to zero-order. Overall, the optimum pH-indicator for the microbial TTIs was bromocresol green, followed by bromocresol purple, bromophenol blue, chlorophenol red, and congo red, in descending rank order.

In conclusion, the choice of pH-indicators was found to be selective to assure effective color development of TTI. Influence of some pre and postfermentative factors. Food Res. Study of a laboratory-scaled new method for the accelerated continuous ageing of wine spirits by applying ultrasound energy.

Delgado-Gonzalez, M. During the ageing of brandies, many physicochem. Because of these reactions, the polyphenolic content of brandies and their content of org. These reactions are slow, and the ageing of high-quality brandies takes several years. In this paper, the development of a system that uses the circulation of the wine distillate through encapsulated American oak chips and the application of ultrasound energy with the aim of producing aged wine spirits has been carried out, and the influences of the operation variables over the characteristics of the produced drink have been measured.

With that proposal, the influence of different powers of ultrasound, and also the influence of the movement of the liquor through oak chips, was detd. Then, applying Youden and Steiner's exptl.

This way, the best spirit produced by this new method of ageing is obtained with a high alc. In addn. Finally, the application of ultrasound energy in large pulses is related with the improvement of two important ageing markers: the intensity of the color and the TPI. Free delivery worldwide. Bestselling Series. Harry Potter. Popular Features. New Releases.

Mathematical Modeling With Excel. Description Mathematical modeling is the use of applying mathematics to real-world problems and investigating important questions about their outcomes. Mathematical Modeling with Excel presents various methods used to build and analyze mathematical models in a format that students can quickly comprehend. Excel is used as a tool to accomplish this goal of building and analyzing the models. Ideal for math and secondary math education majors, this text presents a wide variety of common types of models, as well as some new types, and presents each in a unique, easy-to-understand format.

End-of-chapter exercises ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios. Product details Format Paperback pages Dimensions Other books in this series.