Plotting problems

The point of this excerise is to illustrate that simple graph plotting problems that would not tax a... 

The grand composite curve is obtained by plotting the problem table cascade. A typical grand composite curve is shown in Fig. 6.24. It shows the heat flow through the process against temperature. It should be noted that the temperature plotted here is shifted temperature T and not actual temperature. Hot streams are represented ATn,in/2 colder and cold streams AT iJ2 hotter than they are in practice. Thus an allowance for ATj in is built into the construction. 

Figure 6.30 shows the grand composite curve plotted from the problem table cascade in Fig. 6.186. The starting point for the flue gas is an actual temperature of 1800 C, which corresponds to a shifl ed temperature of (1800 — 25) = mS C on the grand composite curve. The flue gas profile is not restricted above the pinch and can be cooled to pinch temperature corresponding to a shifted temperature of 145 C before venting to the atmosphere. The actual stack temperature is thus 145 + 25= 170°C. This is just above the acid dew point of 160 C. Now calculate the fuel consumption ...

Figure 16.19 shows the grand composite curve plotted from the problem table cascade. The two levels of steam generation are shown. 

An important and expensive problem in surface science occurs in the prevention of the attachment of marine animals such as barnacles to ship surfaces, a process known as biofouling. Baier and Meyer [159] have shown that the Zisman plot can be used to predict biofouling, thus avoiding costly field tests to find a successful coating to prevent biofouling. 

As an extension of Problem 11, integrate a second time to obtain the equation for the meniscus profile in the Neumann method. Plot this profile as y/a versus x/a, where y is the vertical elevation of a point on the meniscus (above the flat liquid surface), x is the distance of the point from the slide, and a is the capillary constant. (All meniscus profiles, regardless of contact angle, can be located on this plot.)... 

Alternatively, data may be plotted as n versus T at constant pressure or as P versus T at constant n. One thus has adsorption isobars and isosteres (note Problem XVII-2). 

A variety of experimental data has been found to fit the Langmuir equation reasonably well. Data are generally plotted according to the linear form, Eq. XVn-9, to obtain the constants b and n from the best fitting straight line. The specific surface area, E, can then be obtained from Eq. XVII-10. A widely used practice is to take to be the molecular area of the adsorbate, estimated from liquid or solid adsorbate densities. On the other hand, the Langmuir model is cast around the concept of adsorption sites, whose spacing one would suppose to be characteristic of the adsorbent. See Section XVII-5B for an additional discussion of the problem. 

The equation of state for a solid film is often ic= b - aa (note Section IV-4D). Derive the corresponding adsorption isotherm equation. Plot the data of Problem 11 according to your isotherm equation. 

Plot the data of Problem II according to Eq. XVII-76 and according to Eq. XVII-79. Comment. 

Construct a v versus t plot for the data of Problem 11 (assume that Table XVII-4 can be used) and calculate the specific surface area of the rutile. 

Use the data of Fig. XVII-1 to calculate qst for a range of p values and, in conjunction with Problem 11, plot st versus n/rim-... 

Use the data of Problem XVII-11 to obtain an MP plot, as in Fig. XVII-30. Comment on the result. 

To see physically the problem of motion of wavepackets in a non-diagonal diabatic potential, we plot in figure B3.4.17 a set of two adiabatic potentials and their diabatic counterparts for a ID problem, for example, vibrations in a diatom (as in metal-metal complexes). As figure B3.4.17 shows, if a wavepacket is started away from the crossing point, it would slide towards this crossing point (where where it would... 

As was said in the introduction (Section 2.1), chemical structures are the universal and the most natural language of chemists, but not for computers. Computers woi k with bits packed into words or bytes, and they perceive neither atoms noi bonds. On the other hand, human beings do not cope with bits very well. Instead of thinking in terms of 0 and 1, chemists try to build models of the world of molecules. The models ai e conceptually quite simple 2D plots of molecular sti uctures or projections of 3D structures onto a plane. The problem is how to transfer these models to computers and how to make computers understand them. This communication must somehow be handled by widely understood input and output processes. The chemists way of thinking about structures must be translated into computers internal, machine representation through one or more intermediate steps or representations (sec figure 2-23, The input/output processes defined... 

Assuming that an equilibrium is now well established, the simulation may be restarted (not newly started) to begin with the sampling of structural and thermodynamic data. In our model case, data acquisition was performed for 3 ns (trajectory data plot not shown). For the production phase, also, the time evolution of the variables mentioned above should be monitored to detect stability problems or con-... 

Plot the probability density obtained from E in Problem 9 as a function of r, that is, simply square the function above with an appropriate scale factor as determined by trial and error. Comment on the relationship between your plot and the shell structure of the atom. 

Changing the constants in the SCF equations can be done by using a dilferent basis set. Since a particular basis set is often chosen for a desired accuracy and speed, this is not generally the most practical solution to a convergence problem. Plots of results vs. constant values are the bifurcation diagrams that are found in many explanations of chaos theory. 

It will be convenient to deal first with the distribution aspect of the problem. One of the clearest ways in which to represent the distribution of sizes is by means of a histogram. Suppose that the diameters of SOO small spherical particles, forming a random sample of a powder, have been measured and that they range from 2-7 to 5-3 pm. Let the range be divided into thirteen class intervals 2-7 to 2-9 pm, 2-9 to 3-1 pm, etc., and the number of particles within each class noted (Table 1.5). A histogram may then be drawn in which the number of particles with diameters within any given range is plotted as if they all had the diameter of the middle of the... 

Note These equations are from Doming, S. N. Morgan, S. L. Experimental Design A Chemometric Approach. Elsevier Amsterdam, 1987, and pseudo-three-dimensional plots of the response surfaces can be found in their figures 11.4, 11.5, and 11.14. The response surface for problem (a) also is shown in Color Plate 13. 

Alternative approaches are to be found in the hterature. Derivations of the above equations are given in numerous texts (2,10—12), which also describe graphical or analytical solutions to the problem. Many of these have direct analogues in other separation processes such as distillation (qv) and hquid—hquid extraction, and use plots such as the McCabe-Thiele diagram or Ponchon-Savarit diagram. 

The vertical position is preferred if the plot space is tight. Horizontal vessels are easier to support and are preferred when large Hquid surge volumes are required. The Hquid level displacement height for a unit volume is much less for a horizontal vessel than for a vertical vessel, which makes the control range shorter than for a vertical vessel. The displacement height per unit volume is only approximately linear on horizontal vessel when the level is near the center line, however. This can be a problem if the normal Hquid level is too low or too high and the instniments are not tuned for quick response. 

Plastic deformation is commonly measured by measuring the strain as a function of time at a constant load and temperature. The data is usually plotted as strain versus time. Deformation strain can be measured under many possible loading configurations. Because of problems associated with the preparation and gripping of tensile specimens, plastic deformation data are often collected using bend and compression tests. 

Such programs generally concentrate on the technical parts of designing an experiment, and provide limited guidance on the important, softer aspects of experimental design stressed in this article. Also, most computer routines do not allow one to handle various advanced concepts that arise frequently in practice, eg, spHt plot and nested situations, discussed in the books in the bibhography. In fact, some of the most successful experiments do not involve standard canned plans, but are tailored to fit the problem at hand. 

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