ENGINEERING ECONOMY - EXAMPLE 7.3 : There are 2 alternatives of investment. Choice 1 : A trader offers you an investment opportunity where your investment of A$15000 presently will be A$18000 after 4 years. Choice 2 : A bank offers you 5 % annual return for your initial investment of A$15000. Question a : What is the equivalent bank payment after 4 years? Question b : By using the concept of equivalence in engineering economy, which is the better choice, between 1 and 2, that will be more profitable after 4 years?

Question 92 - (a) In order to determine the slurry volume (L) in chromatography, arrange the formula using the following parameters : slurry concentration (%), slurry volume (L), settled chromatography medium volume (L), 100. (b) In order to determine the chromatography medium volume (L) in gel filtration chromatography, arrange the formula using the following parameters : sample volume to be processed (L), chromatography medium volume (L), sample volume in percent of total column volume (%), 100.

Question 93 - In thin layer chromatography (TLC), let retention factor Rf = (distance traveled by solute) / (distance traveled by solvent). Silica gel is used as stationary phase which is more polar than the hexane solvent as mobile phase. If the Rf values of 3 solutes A, B and C are 1.5, 0.75 and 1 respectively, compare the polarities of A, B and C with reasons.

ENGINEERING MATHEMATICS - EXAMPLE 8.1 : A local utility burns coal having the following composition on a dry basis : Carbon (C) 83.05 %, hydrogen (H) 4.45 %, oxygen (O) 3.36 %, nitrogen (N) 1.08 %, sulfur (S) 0.7 % and ash 7.36 %. Calculate the ash free composition of the coal with reference to C, H, O, N and S.

Question 94 - The resolution of separation, Rs for chromatography is given by the formula Rs = (difference in retention time) / (average width at the base). In a chromatogram, 3 peaks a, b and c are found. Average widths W at the bases of the solutes are : Wa = 20 s, Wb = 40 s, Wc = 30 s. Resolutions of separation, Rs for solutes b and c in comparison to a are 2 and 4 respectively. The differences in retention times T for b and c in comparison to a are (Tb - Ta) and (Tc - Ta), Ta = Tc - Tb : (a) Form 2 equations involving Rs as a function of Wa, Wb, Wc, Ta, Tb and Tc. (b) Find the values of Ta, Tb and Tc.

ENGINEERING MATHEMATICS - EXAMPLE 8.2 : In the US (United States), one barrel is equal to 42 US gallons and equivalent to 0.15898 cubic metres. One British barrel is equal to 36 Imperial gallons and equivalent to 0.163659 cubic metres. If an oil refinery in England sells 42 Imperial gallons of crude oil to a company in US, how much US gallons of crude oils has been sold?

ENGINEERING MATHEMATICS - EXAMPLE 8.3 : Solve the first order differential equation : (Z + 1)(dy/dx) = xy in term of ln |y| = f(x). Z = (x)(x).

Question 99 - (a) The quantum number m is given by m = -s, -s + 1. If s = 0.5, find the values of m. (b) | T > = (cos T) | V > + (sin T) | H >. The V and H states form a basis for all polarizations. Let cos T = 0.8. (i) If (sin T)(sin T) + (cos T)(cos T) = 1, find the value of sin T. (ii) For | T > = a | V > + b | H >, where a x a represents the probability of | V > and b x b represents the probability of | H >. Which one is more abundant, | V > or | H >? (iii) Find the value of T without using any mathematical tools.

Question 100 - (a) Time evolution in Heisenberg picture, according to Ehrenfest theorem is m (d / dt) < r > = < p >, where m = mass, r = position, p = momentum of a particle. If v = velocity, prove that m < v > = < p >. (b) Lande g-factor is given by Gj = Gl [ J (J + 1) - S (S + 1) + L (L + 1) ] / [ 2J (J + 1) ] + Gs [ J (J + 1) + S (S + 1) - L (L + 1) ] / [ 2J (J + 1) ]. If Gl = 1 and under approximation of Gs = 2, prove by calculation that Gj = (3/2) + [ S (S + 1) - L (L + 1) ] / [ 2J (J + 1) ].

ENGINEERING MATHEMATICS - EXAMPLE 8.4 : Let 1 ^ 1 = 1, 2 ^ 2 = 4, 3 ^ 3 = 27. By using the Excel computer programming - either by Solver or Goal Seek, find the value of v for the Van der Waals equation (P - a / v ^2) (v - b) = RT where a = 18.82, b = 0.1193, P = 2, R = 0.082, T = 5000 for benzene. Describe briefly how to use Solver and Goal Seek in Excel program of computer to find the solution quickly.

UNIT OPERATION - EXAMPLE 9.1 : Which of the sequence below represent a feasible flows of ethanol processing plants using cellulose as starting material? A. raw material -> heat exchanger -> distillation column -> reactor. B. reactor -> distillation column -> raw material -> heat exchanger. C. heat exchanger -> raw material -> distillation column -> reactor. D. raw material -> heat exchanger -> reactor -> distillation column. E. distillation column -> raw material -> reactor -> heat exchanger.

Question 101 - (a) Let | A > = (Aa Ab Ac), | B > = (Ba Bb Bc), | C > = (Ca Cb Cc). Find | A > + | C > - | B > in term of Aa, Ab, Ac, Ba, Bb, Bc, Ca, Cb and Cc. (b) Let d | E > = d (Ea Eb Ec) = (d Ea d Eb d Ec). If | E > = (6 7 8), find the value of 10 | E >.

UNIT OPERATION - EXAMPLE 9.2 : A distillation column separates 10000 kg / hr of a mixture containing equal mass of benzene and toluene. The product D recovered from the condenser at the top of the column contains 95 % benzene, and the bottom W from the column contains 96 % toluene. The vapor V entering the condenser from the top of the column is 8000 kg / hr. A portion of the product from the condenser is returned to the column as reflux R, and the rest is withdrawn as the final product D. Assume that V, R, and D are identical in composition since V is condensed completely. Find the ratio of the amount refluxed R to the product withdrawn D. Hint : Solve the simultaneous equations as follow in order to find the answer (R / D) : 10000 = D + W; 10000 (0.5) = D (0.95) + W (0.04); 8000 = R + D.

UNIT OPERATION - EXAMPLE 9.3 : In the distillation of binary systems by Mc Cabe Thiele method, the equation for the line of top section is given by y = [ R / (R + 1) ] x + XD / (R + 1). 2 points on the line are (0.99, 0.99) and (0, 0.36). Find the reflux ratio of R and XD.

UNIT OPERATION - EXAMPLE 9.4 : Acetone and ethanol are separated using a distillation column with a partial condenser and partial reboiler. An equimolar, sub-cooled liquid feed enters at 100 kmol / hr and condenses 1 mole of vapor for every 6 moles of feed. The separation requires a distillate vapor that is 95 mol % acetone and bottoms liquid that is 5 mol % acetone. The reflux is returned from the condenser to the column as a saturated liquid and the operation is run at (L / V) = 1.4 * (L / V) min. Assume constant overflow conditions. (a) Feed operating line is y = [ q / (q - 1) ] x - z / (q - 1) where z = 0.5 for equimolar liquid mixture of 2 components, q = (L'- L) / F where L' = L + F + (F / 6) for condensation of 1 mole of vapor / 6 moles of feed. What is y = f(x)? (b) The rectifying operating line is y = (L / V) x + (D / V) (xd) where (L / V) min goes through the points A (0.95, 0.95) and B (0.53, 0.69), V = L + D. What is y = f(x)? Let xd = 0.95. (L / V) min is the slope of the 2 points A and B.