Using the Spreadsheet

Testing conditions as per ASTM D1238 for some common polymers  

JVote Numbers and letters in bold denote rows and columns in the spreadsheet. Source-. Reprinted from Ref. 8 with permission from DRI/McCraw-Hill, Milan, Italy. 

Three input values are needed (temperature at which rheogram is desired, known MFI value, and known ASTM condition) before calculations can be performed. The spreadsheet is normally on its default setting of automatic recalculations so that the entire worksheet gets calculated for every change in any cell value. 

To avoid time losses due to unnecessary recalculation, the itaanu option is prefened during data entry and the development of large programs. Therefore, the first step in the present case would be to hold the spreadsheet calculation facility on manual during the simultaneous data input of all three values. This is done through 

After inputting the three values, the automatic recalculation mechanism is activated by using 

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Calculated percentage alcohol = 51.3 per cent, required value 91 per cent. Clearly the initial value selected for a154 was too high too much recycle. Iteration, using the spreadsheet, shows the correct value of a154 to be 0.0053, see Figure 4.19b. 

However, the most appropriate value of the rate constant for each model needs to be determined. This can be determined, for example, in a spreadsheet by setting up a function for R2 in the spreadsheet and then using the spreadsheet solver to minimize R2 by manipulating the value of kA. The results are summarized in Table 5.6. 

Black bodies emit radiation at all wavelengths. Using the spreadsheet, calculate the contribution to the visible spectrum from the cosmic microwave background in the visible region of the spectrum. 

The Excel Solver. Microsoft Excel, beginning with version 3.0 in 1991, incorporates an NLP solver that operates on the values and formulas of a spreadsheet model. Versions 4.0 and later include an LP solver and mixed-integer programming (MIP) capability for both linear and nonlinear problems. The user specifies a set of cell addresses to be independently adjusted (the decision variables), a set of formula cells whose values are to be constrained (the constraints), and a formula cell designated as the optimization objective. The solver uses the spreadsheet interpreter to evaluate the constraint and objective functions, and approximates derivatives, using finite differences. The NLP solution engine for the Excel Solver is GRG2 (see Section 8.7). 

Plot the standard curve using the spreadsheet procedure used in Experiment 18 and obtain the correlation coefficient and the concentrations of the unknowns and control. 

Create the standard curves (one for caffeine and one for benzoate) by plotting peak size vs. concentration. Use the spreadsheet procedure in Experiment 18. Obtain the concentrations of the unknowns and the control. Plot the results for the control sample on the control chart for this instrument posted in the laboratory. 

Using the spreadsheet representation of the CVD flow field (Fig. 2.23), evaluate the strain-rate tensor at the point z = 0.045789474 m and r = 0.026666667 m. Although this is a two-dimensional axisymmetric problem, be aware that there are 0 components in the tensor. 

Thus the equations that we must solve are 12.196 and 12.197, which comprise a set of two coupled first-order differential equations, subject to the boundary conditions, Xj = 0.01395, and X2 = 0.00712 at z = 0 and Xj = X2 = 0 at z = Z, with the unknown fluxes Ni, N2 that must be found. This equation set could easily be solved as a two-point boundary-value problem using the spreadsheet-based iteration scheme discussed in Appendix D. However, for illustration purposes we choose to solve the equation set with a shooting method, mentioned in Section 6.3.4. We can solve the problem as an ordinary differential equation (ODE) initial-value problem, and iteratively vary Ni,N2 until the computed mole fractions X, X2 are both zero at z = Z. 

A simpler method, related to the F test but more direct, to answer the question of which parameters a, b, c are significant is the calculation of the P value for each, using the spreadsheet T distribution function ... 

Finally, we note that programming of a sort is possible using the spreadsheet Macro feature. This allows one to record a sequence of operation (Copy, Move, Sort, Regress, etc.) carried out in the spreadsheet. This sequence is given a name and can then be repeated later by Playing this macro. Macros can be fairly sophisticated since it is possible to use them to branch to different locations, to ran other Macros, and to perform Do loops in a manner as done in Visual Basic, C, or other programming languages. 

Finally a Validation Report should be prepared in response to the Validation Plan to summarize the outcome of validation. Approval of the Validation Report authorizes release of the spreadsheet for use. The spreadsheet should be moved to a protected area to prevent unauthorized or unintentional changes being implemented, and a formal change control process initiated. 

When the spreadsheet is constructed, the displayed contents of Rows 1,3-5,7, and 8 are entered exactly as shown except for the given formulas in Cells B4, D4, F4, D5, and F5. After the cell contents of Row 9 have been entered they are copied into Rows 10 and 11, and the pressures in Column A are then changed to their desired values. The entries in Cells C9-C11 (the initial guesses for V) are the values copied from the adjacent cells in Column B (the values obtained using the ideal gas equation of state). The correct values are then obtained by trial and error for example, the value in Cell C9 would be varied until the value in Cell D9 is sufficiently close to zero, and similarly for Rows 10 and 11. The search is conveniently done using the spreadsheet s [Pg.205]

Use the results of part (b) to determine the values of a and b by a graphical curve-fitting procedure. [Suggestion Use the spreadsheet program from part (b).]... 

Additional columns may be used to store other calculated variables (e g., specific enthalpies). Briefly explain why Q is positive when P = 652 mm Hg and negative when P = 714 mm Hg. (e) In successive rows, repeat the calculation for the same zb and T at several pressures between Pi , and pmax- Generate a plot (using the spreadsheet program itself, if possible) of v versus P. At approximately what pressure is half of the feed stream vaporized ... 

Note One could also use the spreadsheets in POLYMATH or Excel to formulate Table E13-2.1 and to calculate the mean residence time f and variance a. 

The main calculations are performed using the spreadsheet for annual total product cost at 100% capacity. Annual TPC, from the book s web site. 

Copy the value of a variable or a formula in one cell into other cells Execute an iterative calculation using the spreadsheet function... 

Physical properties and/or the equations used to predict physical properties can be stored on spreadsheets. No programming experience is required, and simple calculations are easy to carry out using the spreadsheet software. Numerical data such as tables can be typed into cells, where they are easily seen. Equations can also be typed into cells and are introduced as needed. Labels and units as well as remarks can be added as needed. 

We have now constructed a general-purpose spreadsheet that you may use to make basic statistical calculations. To complete this part of the exercise, select a convenient location, construct a formula to display the number of degrees of freedom, and then add a label in an adjacent cell to identify this important variable. Save the file for future use in problems and laboratory calculations. Use the spreadsheet now to check the calculations in Example 6-1. To clear the data from your worksheet, just click and drag to highlight cells B2 B7, and. strike [Delete]. Alternatively, you may simply click on B2, and begin typing the data. Terminate each piece of data with [ J]. Be sure to delete the data in cells B7 D7. 

In this equation, the number of degrees of freedom is iV — 2, since one degree of freedom is lost in calculating m and one in determining b. The standard deviation about regression is often called the standard error of the estimate. It roughly coiresponds to the size of a typical deviation from the estimated regression line. Examples 8-4 and 8-5 illustrate how these quantities are calculated and used. The spreadsheet calculation of these quantities is illustrated in the Spreadsheet Exercise later in this section. 

Use a spreadsheet to compare the masses of (a) TRIS (121 g/mol), (b) Na2C03 (106 g/moI), and (c) Na2B407 10H2O (381 g/mol) that should be taken to standardize an approximately 0.020 molar solution of HCl for the following volumes of HCl 20.00 mL, 30.00 mL, 40.00 mL, and 50.00 mL. If the standard deviation associated with weighing out the primaiy-standard bases is O.I mg, use the spreadsheet to calculate the percent relative standard deviation that this uncertainty would introduce into each of the calculated molarities. 

These calculations can be completed using the spreadsheet functions. The iteration is controlled using a Visual Basic MACRO. The inverse matrix gives the errors and covariances. The errors in the parameters will be obtained from the inverse matrix. They are (sa)2 = daa S, where S is / o/ o /(u — 2) for the two parameters that are determined from the data. Likewise, (sb)2 = clhh S and sab, the covariance term, is dab S. 

Step 1 In effect you used the spreadsheet to do the molar balances, and you set v yourself. The spreadsheet shows the value oif(v ) for your choice of v, but it does the molar balance anyway. 

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