The document is a set of exam questions for a Chemical Engineering course. It includes 8 questions related to topics like: 1) Using numerical methods like Runge-Kutta, Newton-Raphson, and regression to solve differential equations and find roots. 2) Solving systems of equations using methods like Cramer's rule and Gauss elimination. 3) Modeling and solving reaction kinetics problems using numerical integration and optimization techniques. 4) Estimating parameters for equations of state and heat transfer relationships using regression analysis.

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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

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Code No: RR420803
Set No. 1

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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]

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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]

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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]