Plotting the Equation

Imagine that one wanted to demonstrate the adherence of the kinetic data to the two equations referred to in Problem 1.3. One might do this graphically by plotting the equation of a... 

Similarly, NadiabNisoplotfgxA.m plots the linear and exponential parts separately, first of the two equations (3.16) in terms of xa, and then of (3.11) in terms of y in more detail, while NadiabNisoplotfgxAy, m creates the following three graphs first it repeats the linear and exponential parts plot of (3.16), followed by plotting the equation (3.16) converted to standard form, i.e., converted to an / equal to zero equation. And finally the same is done with equation (3.14). These differing plots are useful when one is trying... 

A model equation for the transformation phenomenon (see following sections), as well as seed coefficients for the equation, are entered into the program code. These seed coefficients are estimates which, after plotting the equation, create a data set... 

Related Calculations. The minimum temperature difference required for nucleate boihng to occur can also be determined by plotting the equations for nucleate-boihng and natural-convection heat-transfer coefficients. The intersection of these two lines represents the required temperature difference... 

This last equation is now in the proton condition. This means that we have eliminated all terms other than Cg, H as pH, and known concentrations and stability constants, allowing us to plot the equation as Cg versus pH. Assuming Cl = 0.01 eq/L, we now introduce values of H and solve for Cg. The results are plotted in Fig. 5.5. The figure shows the inflection point and endpoint at pH 7.0. 

Next, substitute into the charge-balance equation to place it in the proton condition, its proper form for plotting. The equation thus becomes... 

For the first-order case log r plotted against log [r] should yield a straight line with a slope of 1.0. For the second-order case the result should be a straight line of slope of 2.0, in accordance with Eq. (H). A plot of the data in Table 2-4 is shown in Fig. 2-4. While there is some scattering, the points do suggest a straight line of a slope approximately equal to 2.0. For comparison purposes lines with slopes of both 2.0 and 1.0 have been included on the plot. The equation of the solid line (slope 2.0) is... 

Plot the equation A curies (radioactivity unit) and X 25 years. 

By plotting the equation on a Weibull modulus sheet and finding the gradient of the straight line, the Weibull modulus can be found. The... 

In the simplest case, for a pressure drawdown survey, the radial inflow equation indicates that the bottom hole flowing pressure is proportional to the logarithm of time. From the straight line plot ot pressure against the log (time), the reservoir permeability can be determined, and subsequently the total skin of the well. For a build-up survey, a similar plot (the so-called Horner plot) may be used to determine the same parameters, whose values act as an independent quality check on those derived from the drawdown survey. 

Equation 11-30 may be integrated to obtain the profile of a meniscus against a vertical plate the integrated form is given in Ref. 53. Calculate the meniscus profile for water at 20°C for (a) the case where water wets the plate and (b) the case where the contact angle is 40°. For (b) obtain from your plot the value of h, and compare with that calculated from Eq. 11-28. [Hint Obtain from 11-15.]... 

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.)... 

Plot the data according to the BET equation and calculate Vm and c, and the specific surface area in square meters per gram. 

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. 

In accordance with equation (Bl.20.1). one can plot the so-called surface force parameter, P = F(D) / 2 i R, versus D. This allows comparison of different direct force measurements in temis of intemiolecular potentials fV(D), i.e. independent of a particular contact geometry. Figure B 1.20.2 shows an example of the attractive van der Waals force measured between two curved mica surfaces of radius i 10 nun. 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

Remick and Geankoplis made flux measurements for both species in the isobaric diffusion of nitrogen and helium through their tube bundle. Pressures spanned the interval from 0.444 nim, Hg to 300,2 ram Hg, which should cover the whole range between the limits of Knudsen streaming and bulk diffusion control. Then, since K and K, are known in this case, the form of the proposed flux relations could be tested immediately by plotting the left hand side of equation (10.15) against... 

When we draw a scatter plot of all X versus Y data, we see that some sort of shape can be described by the data points. From the scatter plot we can take a basic guess as to which type of curve will best describe the X—Y relationship. To aid in the decision process, it is helpful to obtain scatter plots of transformed variables. For example, if a scatter plot of log Y versus X shows a linear relationship, the equation has the form of number 6 above, while if log Y versus log X shows a linear relationship, the equation has the form of number 7. To facilitate this we frequently employ special graph paper for which one or both scales are calibrated logarithmically. These are referred to as semilog or log-log graph paper, respectively. 

Fig. 3.21 The effect of meniscus curvature on surface tension. Plot of /) against r . y is the surface tension of the meniscus having the mean radius of curvature and y that of a plane surface of liquid, according to Melrose. The value of y/y was calculated by the equation V = /x(l - with a . = 3 a.

It is, however, possible to calculate the tensile strength of a liquid by extrapolation of an equation of state for the fluid into the metastable region of negative pressure. Burgess and Everett in their comprehensive test of the tensile strength hypothesis, plot the theoretical curves of T /T against zjp, calculated from the equations of state of van der Waals, Guggenheim, and Berthelot (Fig. 3.24) (7], and are the critical temperature and critical... 

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