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# Computerapplicationinchemicalengineering Jntu Model Paper{Www.Studentyogi.Com}

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• 1. www.studentyogi.com www.studentyogi.com Code No: RR420803 Set No. 1 IV B.Tech II Semester Regular Examinations, Apr/May 2007 COMPUTER APPLICATION IN CHEMICAL ENGINEERING (Chemical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Apply Runge-Kutta third order metho d to nd an approximate value of y when x =0.2 in steps of 0.1, given that dy/dx = x+y2 and y = 1 when x = 0. [16] 2. Solve by Cramer’s rule, the equations:2x1+5x2+3x3 = 1,-x1+2x2+x3=2,x1+x3+x2= 0. [16] 3. Find the solution to the set of equations shown below. 2 1 - 3 2 - 3 3 + 6 - 4 = 15; 4 1+2 2+3 -3 -4 4 = 10; 5 1+6 2 + 3-12 -4 = 5; 3 1- 2+2 3 +2 4 = 13 using Gauss Elimination metho d. [16] 4. (a) Solve the equation e-x - x = 0 by Newton-Raphson method. (b) How does one choose the initial guess value of the root? [12+4] 5. An elementary liquid phase reaction A + B R+S is conducted in a multiple reactor system in which 100liters capacity CSTR is used as the rst unit and a PFR is used as the second unit. Find the intermediate conversion between the both the units using iterative method. Data: Initial molar ratio of B to A, M =2, Reaction rate constant (k) =0.2 lit/gmol.min, CA0=0.5 gmol/lit and 0=93.3 lit/min. [16] 6. The speci c heat of the Hexane was measured at various temperatures during the heating and given in the following table Temp(T),K 298 350 400 450 500 550 Cp/R 16.24 18.229 20.07 21.84 23.53 25.14 If the relationship between speci c heat and temperature is of the form: Cp/R=A+BT+C 2+D 3 Estimate the coe cients using polynomial regression. What is the value of speci c heat at 700K. [16] 7. (a) Explain the necessary and su cient conditions for the extreme of an uncon- strained function. (b) Determine the nature of stationary point of the function f(x) = -3 5 + 10 3 - 20 [8+8] 8. (a) Compare the Fibonacci method and mo di ed Fibonacci method by computing the number of experiments required to get an accuracy of = 0.01. (b) Find the e ectiveness of Fibonacci method and modi ed Fibonacci metho d
• 2. www.studentyogi.com www.studentyogi.com Code No: RR420803 Set No. 1
• 3. www.studentyogi.com www.studentyogi.com Code No: RR420803 Set No. 2 IV B.Tech II Semester Regular Examinations, Apr/May 2007 COMPUTER APPLICATION IN CHEMICAL ENGINEERING (Chemical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Use Runge- Kutta 4th order method to approximate y at x = 0.1 and x = 0.2 for dy/dx = x+y with x0 = 0 and y0 =1 and h = 0.1. [16] 2. Solve the following equations using Cramer’s rule: x+y+z = 3; x+2y+3z = 4; x+4y+9z = 6. [16] 3. Solve by Gauss elimination method x + y + z = 6.6 x - y + z = 2.2 x + 2y + 3z = 15.2. [16] 4. (a) Find a real ro ot of the equation 3 2 5 = 0 by the Regula-falsi metho d correct to three decimal places. (b) How does one choose the initial value of the root . [12+4] 5. A gaseous mixture has the following composition (in mol / )CH4= 20 / 2 4 =30 / , 2= 50 / . Find the molar volume at 90 atm pressure and 100 C using Vander Waals equation of state with averaged constants of the following type 3- (b’ + RT/b) 2 + (a’/P)V - a’.b’/P =0 where a’, b’ are the average constants a’=2.3 106 atm( 3 )2 , b’=45.0 3/gmol. Use the Newton Raphson method. [16] 6. A new microorganism has been discovered which at each cell division yields three daughter cells. The growth rate data during the batch cultivation is given below Time(t),h 0 .5 1 1.5 2.0 Dry Wt(X),g/l 0.1 0.15 0.23 0.34 0.51 Fit the above data using least square regression in the exponential growth model x=a ebt where a and b are constants. [16] 7. (a) Describe the Newton-Raphson method of nding the extrema of an uncon- strained single variable function. (b) Minimize f(Q) = 4 Q + 16/Q using Newton Raphson method. Start with the rst estimate at Q = 1. [8+8] 8. (a) Compare the Fibonacci method and mo di ed Fibonacci method by computing the number of experiments required to get an accuracy of 0.01. (b) Find the e ectiveness of Fibonacci method and modi ed Fibonacci metho d when the number of experiments is 10. [8+8]
• 4. www.studentyogi.com www.studentyogi.com Code No: RR420803 Set No. 3 IV B.Tech II Semester Regular Examinations, Apr/May 2007 COMPUTER APPLICATION IN CHEMICAL ENGINEERING (Chemical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Using Euler’s method, nd an approximate value of y corresponding to x = 1, given that dy/dx = x + y and y = 1 when x = 0. [16] 2. In a given electrical network, the equations for the currents i1 i2 i3 are 3 1 + 2 + 3= 8; 2 1 - 3 2 - 2 3 = -5; 7 1 + 2 2 - 5 3 = 0. Calculate 1 and 3 by Cramers rule.[16] 3. Develop a step-by-step computational pro cedure to solve the following equation by Gauss elimination method x + 4y - z = -5; x + y - 6z = -12; 3x - y - z = 4. [16] 4. (a) Find the roots of 2 - 25 = 0 numerically using Regula-falsi method. (b) Write the computational procedure to evaluate the roots of the equation. [10+6] 5. For the reaction 2 (g) + 4 2( ) 2 2 ( ) + 4( ) the standard heat of reaction can be expressed as 0 T = H’ + T + ( /2) 2 + ( /3) 3 ; H’=- 148345 j; =-62.54; =46.3510-3 ; = -7 21 × 10-6 . Find the relevant temperature at which standard heat of reaction is equal to -183950j using iterative method. [16] 6. The speci c heat of the Hexane was measured at various temperatures during the heating and given in the following table Temp(T),K 298 350 400 450 500 550 Cp/R 16.24 18.229 20.07 21.84 23.53 25.14 If the relationship between speci c heat and temperature is of the form: Cp/R=A+BT+C 2+D 3 Estimate the coe cients using polynomial regression. What is the value of speci c heat at 700K. [16] 7. (a) Illustrate the importance of optimization techniques in chemical engineering giving at least four examples. (b) Given the function f(x) = 80/x + 20x + 20, nd the stationary points and test them for maxima or minima. [8+8] 8. Find the e ectiveness of preplanned regular interval method, sequential two point regular interval method, sequential dichotomous search and preplanned dichoto- mous search when the number of experiments is 20. [16]
• 5. www.studentyogi.com www.studentyogi.com Code No: RR420803 Set No. 4 IV B.Tech II Semester Regular Examinations, Apr/May 2007 COMPUTER APPLICATION IN CHEMICAL ENGINEERING (Chemical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Using Euler’s method, nd an approximate value of y corresponding to x = 1, given that dy/dx = x + y and y = 1 when x = 0. [16] 2. Solve by Cramer’s rule, the equations:2x1+5x2+3x3 = 1,-x1+2x2+x3=2,x1+x3+x2= 0. [16] 3. Find the solution to the set of equations shown below. 2 1 - 3 2 - 3 3 + 6 - 4 = 15; 4 1+2 2+3 -3 -4 4 = 10; 5 1+6 2 + 3-12 -4 = 5; 3 1- 2+2 3 +2 4 = 13 using Gauss Elimination metho d. [16] 4. (a) Solve the equation 2 - 25 = 0 numerically using Newton-Raphson method. (b) Write the computational procedure to evaluate the roots of the equation . [10+6] 5. Calculate the molar volume of methanol vapor at 400 K and 8 bar by using Redlich- Kwong equation of stateV = [RT P + b - a(V - b) {T0.5 PV(V + b)}] Where a=0.4278 2 Tc2.5 / c; b= 0.0867R c/ c ; c=512.6 K; c =81 bar. Use the regular falsi method. [16] 6. A zero order liquid phase reaction A R is conducted in a constant volume batch reactor and the following data were reported. Fit the data in the zero order rate equation using least square regression technique and nd the rate constant(k). Data: Initial reactant concentration CA0=2gmol/lit, - A=-d A/dt=k. [16] Time(t),min 0 0.25 0.5 0.75 1.0 1.25 1.50 Conversion(X) 0 0.11 0.19 0.31 0.39 0.51 0.60 7. (a) Illustrate the importance of optimization techniques in chemical engineering giving at least four examples. (b) Given the function f(x) = 80/x + 20x + 20, nd the stationary points and test them for maxima or minima. [8+8] 8. Minimize y = (2 - 9)2 0 x 10 for 6 Fibonacci experiments. [16]