Slope of line

Fig. 1. Magaetic hysteresis loop of an initially demagnetized material (curve 1) where poiat A corresponds to (BH), and the slopes of lines B and C, with tangents to curves 1 and 2, represent = B /H and respectively. Terms are defined ia the text.

External reflux ratio = L/D Slope of line from xp ... 

Figure 9 Casson plot, slope of line reflects yield stress value. Interior coating formulation including d.HPMC O, SMAT 0,HEUR.

If the solute i is monodisperse—that is, if no dissociation or aggregation of the (macro)molecules occurs and each one has exactly the same molecular weight at every position in the cell—then M, is the same for all macromolecular species in the solution. If, furthermore, these solute molecules do not interact with each other—that is, if they behave ideally—the term d In yt/dcj = 0. Under these circumstances, In Ci varies hnearly with as shown in hne A of Figure 21.3. If the molecular weight of species i is unknown, it can be determined from the slope of line A, because Equation (21.33) becomes... 

Crystallization kinetics. Figure 5 shows the relation between the dominant particle size Im and the residence time 0 for each run. Im decreases linearly with increase of 0 in log-log plot. The slope of lines decreases with the addition of NaCl. 

Now the k values calculated this way are the slopes of lines joining the individual points to the origin. So for the same magnitude of scatter on the graph the k values calculated for points near the origin (low conversion) will vary widely, whereas those calculated for points far from the origin will show little variation (Fig. 3.25). This fact can make it difficult to decide whether k is constant and, if so, what is its best mean value. 

This is supported by the correlation between the total aerosol volume of particles with diameters in the 0.1- to -fjbva range and the experimentally determined values of hsp obtained using a nephelometer in many studies (e.g., Fig. 9.24). The slopes of lines such as that in Fig. 9.24, however, depend critically on the nature and history of the air mass and can vary by more than a factor of 10 from clean, nonurban air to highly polluted air in the vicinity of sources. For example, Sverdrup and Whitby (1980a) have shown that the ratio of submicron aerosol volume to hsp, which corresponds to the slope of the line in Fig. 9.24, varies from 5 to 80, depending on the nature of the air mass. In addition, the correlation between bsp and fine particles is usually not as clear-cut as seen in Fig. 9.24. 

Fig. 7.6 Crysial structures correlated with atomic charge (slope of lines) for IA-VHA (I—17), IIA-V1A (2- 6). anJ IIIA-VA (13-15) compounds. The abscissa is the difference in electronegativity. (

The slope of line p (called the reaction constant) is a measurement of the sensitivity of such a reaction to the electronic effect of the substituents nevertheless, it can be explained as a proportionality constant pertaining to a given equilibrium (i.e., it depends on the reaction and the solvent), ft relates the effect of substituents on that equilibrium to the effect of those substituents on the benzoic acid equilibrium. That is, if the effect of substituents is proportionally greater than that on the benzoic acid equilibrium, then p > 1 if the effect is less than that on the benzoic acid equilibrium, then p < 1. By definition, for benzoic acid the parameter p is equal to 1 in water at 25°C. Many organic reactions proceed via a series of steps, each of which might have a different reaction constant p hence, to achieve a successful correlation, p must be at least roughly additive. 

Figure 1 Stem Volmer plot of fluorescence intensity of the polymer MPS-PPV (inset) in the presence of methyl viologen (MV2+). slope of line gives Ksv = 1.8 x 107 M-1.

VgdP - SgdT = V dP - SxdT and hence dP/dT, the slope of line CD will be given by ... 

Solution Figure 13.1 shows a representative plot of Af vs. x, for a binary system. Valued of the derivative dAf/dx, are given by the slopes of lines drawn tangent to the curve of Af vs. jc,. One such line drawn tangent at a particular value of x, is shown in Fig. 13.1. Its intercepts with the boundaries of the figure at x, = 1 and x, = 0 are labeled I, and F.. As is evident from the figure, two equivalent expressions can be written for the slope of this line ... 

Measurement of v0 at various substrate levels and known inhibitor concentration yields data in the form shown in Figure 11-10. The various kinetic constants may be obtained as shown in the figure. A convenient way to obtain A) is to plot the values of the slopes of lines such as in Figure 11-10 at several inhibitor concentrations. This replot should be a straight line with an intercept on the x-axis equal to A). A statistically reliable determination of inhibition constants, however, should always involve... 

One of the macroscopic techniques for of establishing the transition has been developed by Platikanov and Rangelova [328,329]. It is based on measurement of the longitudinal specific electrical conductivity of a film obtained between two silver cylinders and the specific electrical conductivity of the initial solution as a function of temperature. The comparison of the results allows to find the temperature at which the CBF/NBF transition occurs. Fig. 3.67 plots these results. Line 1 characterising the temperature dependence of the longitudinal specific electrical conductivity Kf for CBF has the same slope as line 3 which refers to the temperature dependence of the specific electrical conductivity k of the bulk phase. The slope of line 2 which is for NBF is much steeper. The cross-point of lines 1 and 2 indicates the temperature of the CBF/NBF transition at the given electrolyte concentration in the initial solution. Here it is 31.6°C. 

The varying slope of lines A, D, and F (Figure 5) shows that the reaotion rate in stainless steel increases proportionally more rapidly than the pressure. Additional experiments at pressures up to 12 atm. have demonstrated that the reaction is approximately second order with respect to the nitrogen fluoride (7), and similar results have been obtained with copper at 175° C. (8). Studies of the stainless steel system are complicated by the fact that the metal catalyzes the isomerization of N2F2 (7). No detectable isomerization occurs in either glass or quartz. 

Unit cancer risk (UCR) is defined as the sum of the slopes of lines drawn from the lowest apparent effective dose of the chemical throngh zero for each tnmor site... 

It may be that overall montmorillonite equilibrium, whether it be homogeneous or heterogeneous, is not adequately represented by the formulas considered thus far (e.g., 30). However, if equilibrium is carefully approached -from undersaturation and supersaturation over a sufficiently broad range of solution conditions, it whould be possible to accurately determine the slopes of lines similar to those shown in Figures 3 and 4. These slopes represent the coefficients in appropriate dissolution equations. Thus, it seems likely that proper equations can... 

Considering that dissociation occurs upon volatilization, the temperatures can be correlated extremely well on a In P vs (1/rd.voi) plot, where P is the total system pressure and T a.voi decomposition temperature, as the case dictates. Such a plot is shown in Fig. 11. Since the Clausius-Clapeyron relation for vapor pressure of pure substances shows an exponential dependence on temperature, TVoi was considered a pseudo-boiling point at the respective system pressure. For a substance that vaporizes congruently to its gaseous state, the slope of lines on a In P vs (l/Tvoi) plot represents the enthalpy of vaporization. Indeed, the enthalpy of vaporization calculated from the slope on a In P vs (l/TVoi) plot for the B-O2 system (360 kJ/mol) agrees exactly with the value calculated by using... 

The rate constants are estimated by the slopes of lines fitted by a least squares method and listed in Table 1. It is concluded that a two-step first-order kinetic behavior dominates in the surface sorption of U(VI). The relatively slower second-step may be due to such effects as a diffusion-controlled sorption onto the fracture surface of micropores and a mineral dissolution of the granite surface [19], It is noticed from Table 1 that the reaction rates do not greatly depend upon pH although the amount of U(VI) sorbed onto the granite surface is greatly dependent on pH. 

Note that on the x-t plane, the slopes of lines are the reciprocal of velocity therefore, the higher the slope, the lower the velocity, and vice versa. Also, the x-t diagram shows the phenomena in laboratory coordinates so shock velocities indicated by these slopes are laboratory, or Eulerian velocity. 

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