Intercepts, graphs

A straight line may be fitted to the (X, Y) or (X, Y) pairs of data when plotted on log-log graph paper from which the slope N and the intercept log K with X = 1 may be read. Alternatively, the method of least squares may be used to estimate the values of K and N, giving the best fit to the available data. 

Interception with the zero voltage axis, which represents friction and windage losses, may be found by plotting a second graph with the square of the voltage as the abscissa and the watts as the ordinate (Figure 11.6). 

It is clear that a graph of ln(V j-) or In(k ) against 1/T will give straight line. This line will provide actual values for the standard enthalpy (AH ), which can be calculated from the slope of the graph and the standard entropy (AS ), which can be calculated from the intercept of the graph. These types of curves are called van t Hoff curves and their important characteristic is that they will always give a linear relationship between In(V r) and (1/T). However, it is crucial to understand that the distribution... 

Figure 7 Graph of Intercept and Slope from [Log(V r(T))/Number of CH2 Groups Curves] for a Series of -Alkanes/ the Reciprocal of the Absolute Temperature...

A graph of l/v versus S is plotted and the slope is 1 IK2ke0. There is an intercept in the graphical presentation to identify another constant. From the above equation, K2 can be calculated, which is similar to, Smax, where. S m lx means that the substrate concentration gives the maximum rate. 

Equation (4.4) indicates that at low temperatures, a graph of Cp.m/T against T2 should be a straight line with an intercept of zero at T = 0. Figure 4.3 shows such a graph for glucose, where the lowest measurement is at approximately 7.5 K (T2 = 56 K2). A straight-line relationship is obtained below T= 14 K... 

The extrapolation of a graph of LHS against I,1/2 (with the aid of the Debye-Hiickel limiting law) to I 2 = 0 gives an intercept with a value RT/F) n Kw. As a final example, consider the cell... 

Since a Henry s law standard state has been chosen for all three solutes, a graph of LHS against I [2 extrapolated to I 2 = 0 gives - (RT/F) n KA as the intercept. 

Equation (10.160) predicts that a graph of Cy,m/T against T2 should be a straight line with intercept at T = 0 since... 

What does tins equation tell us Because the kinetic energy of the ejected electrons varies linearly with frequency, a plot of the kinetic energy against the frequency of the radiation should look like the graph in Fig. 1.17, a straight line of slope h, the same for all metals, and have an extrapolated intercept with the vertical axis at — horizontal axis (corresponding to zero kinetic energy of the ejected electron) is at fI>/6 in each case. 

Here b is the intercept of the line with the y-axis (Fig. 3), the value of y when x = 0. The slope of the graph, its gradient, is m. The slope can be calculated by choosing two points, x, and x2, and their corresponding values on the y-axis, yj and y2, and substituting the values into the formula... 

We determine the value of [rj] experimentally by making measurements on a series of polymer solutions and plotting a graph of (p - iift/riQ c against c. This gives a straight line with intercept at [p]. The value of [p] is characteristic of the isolated polymer molecule in solution, because of the extrapolation to infinite dilution, and is a fimction of temperature, pressure, polymer type, solvent, and (most important of all in the present context) relative molar mass. 

Solution The classic way of fitting these data is to plot ln( /7 ) versus T" and to extract and Tact from the slope and intercept of the resulting (nearly) straight line. Special graph paper with a logarithmic j-axis and a l/T A-axis was made for this purpose. The currently preferred method is to use nonlinear regression to fit the data. The object is to find values for kQ and Tact that minimize the sum-of-squares ... 

Equation leads to a linear graph plotting In k along the y axis vs. j T along the x axis gives a straight line with a slope of - 5 a /i and an intercept of In A. Thus, A and E can be evaluated after k has been measured at several different temperatures. Example shows how this is done. 

Find the slope and y-intercept of the best-fit line on the frequency versus energy graph. To calculate the slope, choose two points (iq. j ) and (v2, E2) that are well separated on the... 

The actual data, including replicates, mean, and range, in tabular form should follow, accompanied by a brief discussion of the data. It is important to explain any out-of-specification data. Statistical analyses for all parameters, which lend themselves to such analyses along with conclusions, should be incorporated into the document at this point. These statistical analyses should be accompanied by the results of experiments conducted to determine the poolability of batches, or commonality of slopes and intercepts of individual batches. Graphs of these data should be included as part of the documentation. 

The form of this equation shows that a graph of log k versus p/L, should be linear with a slope of —n and an intercept of log C. Dissociation of the acid produces the anion hr that accepts protons from water, as shown in the equation... 

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