Representing Data

When you analyze data, you may set up an equation and solve for an unknown, but this is not the only method scientists have for analyzing data. A goal of many experiments is to discover whether a pattern exists in a certain situation. Does raising the temperature change the rate of a reaction Does a change in diet affect a rat s ability to solve a maze When data are listed in a table such as Table 2-6, a pattern may not be obvious. 

Using data to create a graph can help to reveal a pattern if one exists. A graph is a visual display of data. Have you ever heard the saying, A picture is worth a thousand words  

What do circle graphs and bar graphs have in common  

When the mass of a material is plotted against volume, the slope of the line is the density of the material. Do the CHEMLAB at the end of the chapter to learn more about using a graph to find density. 

Making and Using Graphs Use the steps below and the data to make a line graph. 

Graphs visually depict data, making it easier to see patterns and trends. 

Analyze What percent of the chlorine sources are natural What percent are manufactured compounds  

This graph shows various dietary sources of the element magnesium. Magnesium plays an important role in the health of your muscles, nerves, and bones. 

Personal Tutor For an online tutorial on graphing, visit qlencoe.com. 

A graph is a visual display of data. Representing your data in 

If a best fit line is straight, there is a linear relationship between the variables. This relationship can be described by the steepness, or slope, of the line. If the line rises to the right, the slope is positive. A positive slope indicates that the dependent variable increases as the independent variable increases. If the line falls to the right, the slope is negative. A negative slope indicates that the dependent variable decreases as the independent variable increases. You can use two data points to calculate the slope of a line. 

Calculating the Slope of a Line from Data Points 

Calculate the slope of a line that contains these data points  

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It is worth noting that if field development using horizontal wells is under consideration, then horizontal appraisal wells will help to gather representative data and determine the benefits of this technique, which is further discussed in Section 9.3. 

Now, we can make the comparison beween the real defect signal and the simulated one which have been computed by solving the linearized direct problem. The measurements were made at 300,150,50 kHz. The flaw is a notch of 8mm length, 1mm width, and 1mm depth. Representative data (300 kHz) for the notch-shaped flaw are shown in Fig. 3. 

Alkylation by diazoalkanes gives more N-substituted product when the reaction goes through an S l transition state. Representative data are given in Table Vll-lOa. and they are discussed in Ref. 101. 

The information given for the commercial oils represents data critically selected from pubUshed rehable sources or, in some cases, analyses performed in the authors laboratories on authentic oil samples. These data are provided as a general guide to composition only and are not meant to be exclusive of analytical results obtained by other researchers on similar oils. Where the Hterature provides ranges of composition, these have, in several cases, been included. Many variables affect the composition of essential oils. 

Binary Alloys. Aluminum-rich binary phase diagrams show tliree types of reaction between liquid alloy, aluminum solid solution, and otlier phases eutectic, peritectic, and monotectic. Table 16 gives representative data for reactions in tlie systems Al—Al. Diagrams are shown in Figures 10—19. Compilations of phase diagrams may be found in reference 41. 

Theoretical equation forms may be derived from either kinetic theory or statistical mechanics. However, empirical and semitheoretical equations of state have had the greatest success in representing data with high precision over a wide range of conditions (1). At present, theoretical equations are more limited in range of appHcation than empirical equations. There are several excellent references available on the appHcation and development of equations of state (2,3,18,21). 

It is common that compressor manufacturers provide data for the ratio of the heat rejected at the condenser to the refrigeration capacity as shown in Fig. 11-89. The solid line represents data for the open compressors while the dotted hne represents the hermetic and accessible compresors. The difference between sohd and dotted line is due to all losses (mechanical and elec trical in the electrical motor). Condenser design is based on the value ... 

Pressures can be specified at any level below the safe working pressure of the column. The condenser pressure will be set at 275.8 kPa (40 psia), and all pressure drops within the column will be neglected. The eqnihbrinm curve in Fig. 13-35 represents data at that pressure. AU heat leaks will be assumed to be zero. The feed composition is 40 mole percent of the more volatile component 1, and the feed rate is 0.126 (kg-mol)/s [1000 (lb-mol)/h] of saturated liquid (q = 1). The feed-stage location is fixed at stage 4 and the total number of stages at eight. 

Testing of plates and other devices is carried out by Fractionation Research, Inc. for industrial sponsors. Some of the test data for sieve plates have been published for the cyclohexane//i-heptane and isobu-tane//i-butane systems. Representative data are shown in Fig. 14-43. These are taken from Sakata and Yanagi Jn.stn. Chem. Engis. Symp. See. No. 56, 3.2/21 (1979)] and Yanagi and Sakata [Jnd. Eng. Chem. Proc. Des. Devel, 21, 712 (1982)]. The column diameter was 1.2 m, tray spacing was 600 mm, and weir height was 50 mm. 

Quantities of Solid Wastes Representative data on the quantities of sohd wastes and factors affecting the generation rates are considered briefly in the following paragraphs. 

Leachate in landfills. Leachate may be defined as hquid that has percolated through sohd waste and has extracted dissolved or suspended materials from it. In most landfills, the liqiiid portion of the leachate is composed of the liquid produced from the decomposition of the wastes and liquid that has entered the landfill from external sources, such as surface drainage, rainfall, groundwater, and water form underground springs. Representative data on chemical characteristics of leachate are reported in Table 25-72. 

Table 27-7 shows representative data for hquid fuels from tar sands, oil shale, and coal. 

A wide range of caibocation stability data has been obtained by measuring the heat of ionization of a series of chlorides and cafbinols in nonnucleophilic solvents in the presence of Lewis acids. Some representative data are given in Table 5.4 These data include the diarylmediyl and triarylmethyl systems for which pX R+ data are available (Table 5.1) and give some basis for comparison of the stabilities of secondary and tertiary alkyl carbocations with those of the more stable aryl-substituted ions. 

Table 7.3.1-1 shows spreadsheet headings and a row of representative data. 

The failure events were obtained from Savannah River Plant sources such as Reactor Incident Reports, daily logs, and operating summaries. The records include over 4,400 events going back to 1970 for an effective average of 3 operating nuclear reactors. Some entries represent data averaging about 110 reactor years experience accumulated since operation began. 

The physical properties of ionic liquids can often be considerably improved through the judicious addition of co-solvents [55-58]. Flowever, surprisingly, this approach has been relatively underutilized. Flussey and co-workers investigated the effect of co-solvents on the physical properties of [EMIM]C1/A1C13 ionic liquids [55, 56]. They found significant increases in ionic conductivity upon the addition of a variety of co-solvents. Figure 3.6-5 displays representative data from this work. The magnitude of the conductivity increase depends both on the type and amount of the co-solvent [55, 56]. 

Programmed computer. Represents data input plus calculation time, sometimes multiple. Checking only for Design calculations. 

Fair [183] relates sieve trays and includes valve tray remarks to the extensive work done for bubble cap trays. Figure 8-137 and 8-139 show flooding data for 24-in. spacing of bubble cap trays from [81] and represents data well for 36-in. diameter columns, and is conservative for smaller columns. Fair s work has been corrected to 20 dynes/ cm surface tension by ... 

Continuous-Wave Transmission. Anadrill, a subsidiary of Schlumberger, markets a tool which produces a 12-Hz sinusoidal wave downhole. Ten-bit words representing data are transmitted by changing or maintaining the phase of the wave at regular intervals (0.66 s). A 180° phase change represents a 1, and phase maintenance represents a 0. 

Table 6.2 lists some representative data for the hydrogenation of different alkenes, showing that alkenes become more stable with increasing substitution. 

Another significant feature found recently is that the effect of the chain length on the field-effect mobility is much less pronounced than indicated in earlier reports [68, 74]. The increase from 4T to 6T corresponds to about a factor of ten, while that from 6T to 8T is only two (the low mobility measured for the dihexyl-substituted 8T must be ascribed to the difficulty in synthesizing and purifying this compound 75 J). Representative data arc gathered in Table 14-1. Also note that the effect of alkyl end substitution is reduced by a factor of two to three (as compared to up to 1000 in earlier reports 68 ). 

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