Spreadsheets problem table

The construction of the problem table to find the minimum utility requirement and the pinch temperature is facilitated by using a spreadsheet. The calculations in each cell are repetitive and the formula can be copied from cell to cell using the cell copy commands. 

Note that both problems can be completed using built-in iteration and convergence routines on a spreadsheet. NPW tables can also be used to converge on the final solution. 

Spreadsheet problem] Enter two columns of values that are the a and b coefficients in Table 2.1 for all diatomic and triatomic molecules. Evaluate V, T, and for each gas. 

Spreadsheet problem] Assuming that the van der Waals equation of state holds for ammonia, and using the coefficients for ammonia in Table 2.2, find Equation 4.7). Enter a column of data corresponding to 20 values in a range of volumes for 1 mol of ammonia 0.01,0.02,0.03 L, and so on. Evaluate the pressure that satisfies the equation of state at the critical temperature for each of these pressures. Use the data to make a plot of the critical temperature P-V isotherm. 

Spreadsheet problem] Using values in Table 4.1 for N2O and CI2, apply Equation 5.58 to find the boiling points for when the mole fraction of a solute, Xj, is 0.05, 0.1, 0.15, 0.2,..., 0.95. If a solution were formed with N2O and CI2, at what mole fraction values would the boiling point temperature curves for the two species cross (Determine the eutectic point by plotting both sets of temperature values against mole fractions.)... 

Additionally, solutions to problems are presented in the text and the accompanying CD contains computer programs (Microsoft Excel spreadsheet and software) for solving modeling problems using numerical methods. The CD also contains colored snapshots on computational fluid mixing in a reactor. Additionally, the CD contains the appendices and conversion table software. 

Example 11-1 Unknown Velocity and Unknown Diameter of a Sphere Settling in a Power Law Fluid. Table 11-1 summarizes the procedure, and Table 11-2 shows the results of a spreadsheet calculation for an application of this method to the three examples given by Chhabra (1995). Examples 1 and 2 are unknown velocity problems, and Example 3 is an unknown diameter problem. The line labeled Equation refers to Eq. (11-32) for the unknown velocity cases, and Eq. (11-35) for the unknown diameter case. The Stokes value is from Eq. (11-9), which only applies for - Re,pi < 1 (e.g., Example 1 only). It is seen that the solutions for Examples 1 and 2 are virtually identical to Chhabra s values and the one for Example 3 is within 5% of Chhabra s. The values labeled Data were obtained by iteration using the data from Fig. 4 of Tripathi et al. (1994). These values are only approximate, because they were obtained by interpolating from the (very compressed) log scale of the plot. 

Crystal Ball can deal with spreadsheets that contain no random variables, and OPTQUEST can be applied to deterministic optimization problems arising from such spreadsheets. Table 10.11 shows the performance of OPTQUEST applied to the two-variable, one-constraint problem defined in Equations (10.7), which was solved by an evolutionary algorithm in Section 10.5 to six-digit accuracy in 1000 iterations. OPTQUEST finds the same solution with similar effort. 

The last two columns show Tpftr and TcSTRi so one can simply read Ca(j) and T(t) fi om Table 5-1, and, since this is the same problem worked previously, the previous graphs can be plotted simply from this spreadsheet (see Figure 5-10). 

This problem just begs to be organized. A spreadsheet would be a big help here. But the next best thing is a table showing the item name, the number of items in a case, the cost per case, and a representation of the number of cases ordered. Because the number of cases of cookies and gum is the same, let the number of cases of these items be represented by g. The number of cases of M M s is 2g. The number of cases of pretzels is 2g- 2 and the number of cases of Twix is 2g- 5. Table 14-1 shows all the entries. 

Ilk 6-8 Solving Equilibrium Problems with a Concentration Table and a Spreadsheet... 

It should generate an inlet-outlet enthalpy table based on elemental species at 25 C as references and then calculate the required heat transfer to or from the reactor, 2(kJ). The spreadsheet should be tested using the species and reactions of Problem 9.21 and should appear as shown below. (Some of the input data and calculated results are shown.)... 

Use a circuit with Re = 10 Qcm, Rf = 100 Ocm, and Qi = 20 iF/cm to verify the equations given in Table 22.1. This problem requires use of a spreadsheet program such as Microsoft Excel or a computational programming environment such as Matlab . 

Prepare a spreadsheet similar to the one shown in Figure 3-7 for the gravimetric determination of nickel using dimethylglyoxime. See Section 37B-3 for details. Use the worksheet from Problem 3-9 to calculate the molar mass of Ni(DMG)2 if it is available. 3-4. Write an Excel formula using the FIND and MID functions to eliminate the square brackets and the uncertainty from the atomic mass of lithium in the lUPAC table and display the numeric characters of the atomic weight. 

To solve this problem, prepare the spreadsheet as shown in Table 3.2. 

Use a spreadsheet program to calculate and plot the current-potential curve for this system scanning from the anodic background limit to the cathodic background limit. Take the appropriate standard potentials from Table C.l and values for other parameters (mo, a,. .. ) from Problem 3.3. 

At this point we have all the pieces necessary to ascertain the fermentation times and cycle times corresponding to the three values of the half-saturation constant indicated in the problem statement. These calculations are readily accomplished using a spreadsheet based on equations (H)-(K). The results are summarized in the following table. 

For Problems 4.30-4.38, use either a program similar to that in Table 4.1, a spreadsheet, or a computer-algebra system such as Mathcad. 

H3. A feed containing 30 mol% isobutane, 25% n-pentane, and 45% n-hexane is flashed at a drum pressure of 50 psia and drum tenperature of 650°R. Find V/F, liquid mole fractions, and vapor mole fractions. Use Eq. f2-301 and parameters in Table 2-3. Use a spreadsheet to solve this problem (Turn in two copies of the spreadsheet—one with numbers in the cells and one with equations in the cells.)... 

If VLE data are available in equation form, spreadsheet calculations can also be used for multiconponent flash distillation. These calculations are illustrated for a chemical mixture that follows Eq. 12-161 for Problem 2.D16. First, the spreadsheet is shown in Figure 2-B3 with the equations in each cell. Cells B3 to B6, C3 to C6, D3 to D6, E3 to E6, F3 to F6, and G3 to G6 are the constants for Eq. (2-161 from Table 2-3. Conditions for the operation are input in cells B7, D7, and F7, and the feed mole fractions are in cells B8, C8, F8, and G9. Eq. 12-161 is programmed for each conponent in cells BIO, Bll, B12, and B13. Then the liquid mole fractions are determined fromEq. 12-381 in cells B15 to B18. These four numbers are summed in cell B19. The Rachford-Rice terms from Eq. 12-421 for each conponent are calculated in cells B20 to B23, and the sum is in B24. 

HI. [VBA required] Using the spreadsheet in Appendix B of Chapter 4 or your own spreadsheet, solve the following problem. A methanol water mixture is being distilled in a distillation column with a total condenser and a partial reboiler. The pressure is 1.0 atm, and the reflux is returned as a saturated liquid. The feed rate is 250 kmol/h and is a saturated vapor. The feed is 40 mol% methanol. We desire a bottoms product that is 1.1 mol% methanol and a distillate product that is 99.3 mol% methanol. L/D = 4.5. Find the optimum feed stage, the total number of stages, D and B. Assume CMO is valid. Equilibrium data are available in Table 2-7. Use Excel to fit this data with a 6th-order polynomial. After solving the problem, do What if simulations to see what happens if the products are made purer and if L/D is decreased. 

The spreadsheet results and the VBA program for ternary distillation calculations with constant relative volatility fSection 5.2.1 are shown in Figure 5-Al and Table 5-Al. If you are not familiar with VBA look at Appendix B of Chapter 4. The problem solved is to determine the number of stages and the optimum feed stage for the distillation of 100 mol/h of a saturated liquid feed that is 30 mol% A, 20 mol% B, and 50 mol% C. L/D = 1, and the desired fractional recoveries are B in distillate = 0.99 and C in bottoms = 0.97. Component A = benzene, component B = toluene, and conponent C = cumene. The constant relative volatilities with respect to toluene as the reference are = 2.25, Qbb = 1.0, and a B . 21. By trial and error, the optimum feed stage was determined to be the second stage from the top (the total condenser is not counted as a stage). 

H3. Usually, relative volatilities are not constant, and determination of the residue curve requires a bubble-point calculation at each time used to integrate Eq. (8-28) to determine the temperature T and the vapor mole fractions. The bubble-point calculation was illustrated in Exanple 5-3 for light hydrocarbons. The K values for these conpounds can be determined from Eq. (2-161 with the constants tabulated in Table 2-3. Develop a spreadsheet that can be used to determine the residue curves for any three of the following light hydrocarbons i-butane, n-butane, i-pentane, n-pentane, and n-hexane. Note If Euler s method, Eq. (8-291. is used, the tolerance on the sum of the yy values must be quite small (e.g., E -9). Find the residue curve for the following problems. 

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