Assignment No 1.

Assignment No 01 Chemical Engineering 5th Semester (Fall – 2009) Computer and Numerical Methods in Chemical Engineering (ChE-331) Q1. The function f ( x ) = x is tabulated as follows: x 1.3 1.5 1.14018 1.22474 f (x )

1.7 1.30384

Use linear and quadratic interpolation to estimate 1.38 . Also find the upper and lower bounds for the truncation error in P1 (1.38) and P2 (1.38) . 2

Q2. The function f ( x ) = e x is tabulated as follows: x 0.50 0.52 0.54 1.28403 1.31049 1.33857 f (x ) Use linear and quadratic interpolation to estimate f (0.527 ) . Also find the upper and lower bounds for the truncation error in P1 (0.527 ) and P2 (0.527 ) . Q3. Use the table: x 0.2 0.4 0.6 0.199556 0.396461 0.588119 sin x to estimate sin 0.48 by linear interpolation. Also find the upper and lower bounds for the truncation error in this computation. Q4. Use interpolating polynomials to estimate the population figure (in millions) of the region on the basis of the following census figures: Year: 1971 1981 1991 2001 294 315 319 353 Population: for the year: (a ) 1975

(b ) (c )

1987 1998

Q5. Use interpolating polynomials to estimate the production figure (in tons) of the steel on the basis of the following data: Year: 1991 1993 1995 1997 1999 112.2 117.1 130.4 Production of steel: 150.1 118.8 for the year: (a ) 1992

(b ) (c )

1996 2005

2001 146.3

Q6. The following values of the pressure P lb

and the temperature T degrees ft 2 Fahrenheit of steam at maximum density are given. Find the pressure when the Temperature is 147 0 F .

Temperature T Pressure P

131

140

149

158

327.0

414.3

520.6

649.1

Q7. The population of a certain town is shown in the table below. Estimate the population figure for the year 1925 on the basis of the following data: Year

1921

1931

1941

1951

Population in thousands

19.61

39.65

58.81

77.21

Q8. The following reaction data has been obtained from a simple Decay reaction A → B Time in minutes

0

3

6

9

Concentration in moles/liter

100

65

55

49

Find the concentration in moles per liter when the time is 2 minutes.