CHEMICAL MATERIAL BALANCE – EXAMPLE 2.6 : According to Raoult's law for ideal liquid, x (PSAT) = yP where x is mole fraction of component in liquid, y is mole fraction of component in vapor, P is overall pressure and PSAT is saturation pressure. A liquid with 60 mole % component 1 and 40 mole % component 2 is flashed to 1210 kPa. The saturation pressure for component 1 is ln (PSAT) = 15 - 3010 / (T + 250) and for component 2 is ln (PSAT) = 14 - 2700 / (T + 205) where PSAT is in kPa and T is in degree Celsius. By assuming the liquid is ideal, calculate (a) the fraction of the effluent that is liquid; (b) the compositions of the liquid and vapor phases. The outlet T is 150 degree Celsius.
CHEMICAL MATERIAL BALANCE – ANSWER 2.6 : (a) For component 1, ln (PSAT) = 15 - 3010 / (150 + 250) = 7.475, PSAT = 1763 kPa. For component 2, ln (PSAT) = 14 - 2700 / (150 + 205) = 6.394, PSAT = 598 kPa. Let x(1) PSAT(1) = y(1) P, x(2) PSAT(2) = y(2) P, then x(1) PSAT(1) + x(2) PSAT(2) = [ y(1) + y(2) ] P = P, x(1) (1763) + [ 01 - x(1) ] (598) = 1210, x(1) (1763 - 598) = 1210 - 598, x(1) = 0.525, x(2) = 1 - x(1) = 0.475. (b) y(1) = x(1) PSAT(1) / P = 0.525 (1763) / 1210 = 0.765, y(2) = 1 - y(1) = 0.235. Overall mass balance is assumed 1 mole for F = V + L where F is incoming mole, V is flashed vapor in mole and L is outgoing liquid in mole. For component 1, zF = xL + yV then 0.6(1) = 0.525 L + 0.765 (1 - L), then L = 0.6875, V = 1 - L = 0.3125. Let z to be 60 mole %. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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QUANTUM BIOLOGY - EXAMPLE 33.10 : The wavefunction starts out in a superposition of possible states in a closed black box like this : Ψ (kitty) = 0.7071 Ψ (alive) + 0.7071 Ψ (dead) where Ψ (kitty) = wavefunction of a kitten, Ψ (alive) = wavefunction of a living kitten, Ψ (dead) = wavefunction of a dead kitten. By prediction and calculation, find the probability of : (a) a living kitten inside the black box; (b) a dead kitten inside the black box.
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Question 90 - In the calculation of the growth of bacteria, absorbance, A in spectrophotometry is used. According to Beer-Lambert Law, A = e x l x c where A is the absorbance of the solution (no unit), l is the distance of light travels through the solution (in cm), e is the molar absorptivity or the molar extinction coefficient [ in L / (mol.cm) ]. For a particular solute and fixed path length : As / Ao = Cs / Co where Ao is the observed signal for a known concentration Co, and As is the observed signal for a sample concentration Cs. (a) For a cell concentration of 560 cells / mL, a spectrophotometre gives an absorbance reading of 1.0. A mixture of concentration 3600000 cells / mL can be diluted in several operations, with each operation having a dilution of 1:20. How many dilutions should be made so that the concentration of this mixture can be calculated within a range of A = 0.0 to 1.0. (b) In another experiment, a sample tube of 1 cm in width is used. Let A = 0.06 and e = 0.0012 ml / (cell.cm). Find the cell concentration of the sample.
Question 42 - According to Margules Equation, P = x(1) p(1) g(1) + x(2) p(2) g(2) for a two-component mixture where P is bubble pressure, x is mole fraction, p is saturation pressure, g is constant given by ln g(1) = x(2) A x(2). Find the value of A as a constant when P = 1.08 bar, p(1) = 0.82 bar, p(2) = 1.93 bar in a 50 : 50 mole fraction mixture. Estimate the pressure required to completely liquefy the 30 : 70 mixture using the same equation, by proving P = 1.39 bar. Take note that ln g(2) = x(1) A x(1), ln g(1) = x(2) A x(2).
In a Laplace Transform Table, the Laplace transfer function of f(t) is F(s). When d(t) = f(t) then 1 = F(s). When x(t) = f(t) then X(s) = F(s). If d(t) is the impulse of a spring when d(t) = kx(t), then derive the equation for the impulse of a spring as X(s) in term of k. Next question : A controller has a transfer function a and the other controller has a transfer function b. The overall transfer function of both controllers is ab. What is the transfer function overall when both controllers have similar transfer function 1 / (Cs k)?
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.33 : An engineering corporation that produces a type of healthy food has A number of shares of $B preferred stock and C number of shares of $H common stock outstanding. In a typical financial year, let the net income obtained = D. The amount retained by the corporation = E. (a) Calculate the amount of money distributed to the shareholders if : (i) D > E; (ii) D = E; (iii) D < E. (b) Let preferred dividend = F, common dividend = G, CH > G. Find the values of F and G, in term of A, B, D and / or E when : (i) (D - E) > AB; (ii) (D - E) < AB; (iii) (D - E) = AB.
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