ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.3 : (a) In the M / M / 1 queue that happens with randomness, let State 0 = the queue and server are empty, State 1 = the server is in use and the queue is empty, State 2 = the server is in use and 1 is in the queue, State 3 = the server is in use and 2 in the queue. Let P (0) = probability of State 0, P (1) = probability of State 1, P (2) = probability of State 2, P (3) = probability of State 3 and so on. If c = constant, P (1) = c P (0), P (2) = c [ c P (0) ], P (3) = c { c [ c P (0) ] }, write an equation that involves P (N), P (N + 1) and c. (b) Let L = market price of risk, r = riskless rate, m = expected return, s = volatility. Given that L = (m - r) / s related to oil prices, expected return = 12 %, s = 20 %, riskless rate = 8 %, calculate the market price of risk.
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.3 : (a) P (1) = c P (0), P (2) = c [ c P (0) ] = c P (1), P (3) = c { c [ c P (0) ] } = c P (2). Then P (N + 1) = c P (N). (b) Let m = 12 %, r = 8 %, s = 20 %, then L = (m - r) / s = (12 - 8) / 20 = 4 / 20 = 1 / 5. 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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Question 64 – According to a heuristic of chemical engineering plant design, assume a pressure difference dP = 4 psi for each 10-ft rise in elevation. A pump is needed to pump liquid from a storage tank at a lower elevation to a heating tank at a higher elevation with the elevation difference of 60 ft. (a) Find the pressure loss due to such elevation. (b) If the required minimum inlet pressure to the heating tank is 9 psi, with 1 control valve is installed between pump and heating tank, what is the dP minimum required for the control valve and the entrance to the heating tank when the heuristic mentions that at least 10 psi is required for the control valve? (c) The pressure at the inlet of the pump is 8 psi and the flowrate of the liquid produces pressure head of 50 psi. What is the total pressure produced by the pump? (d) Assume a pipeline dP of 2 psi / 100 ft for liquid flow in a pipe according to heuristic, what is the approximate maximum length of the pipe in ft that can be installed between the pump and the heating tank?
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QUANTUM COMPUTING - EXAMPLE 32.2 : (a) If | 001 > = | 1 >, | 111 > = | 7 >, find the 2 possible values of ( | 001 > + | 1 > + | 7 > ) ( | 111 > ). (b) In quantum money, a duplicate will have probability P of passing the verification test of a bank, if the total number of photons on the bank note is N. The would be counterfeiter has a probability p of success in duplicating the quantum money correctly for each photon. Guess the relationship of P, p and N as a mathematical formula involving natural logarithm ln.
Question 91 - In the application of Theory of Spectrometry in spectrophotometer, let n = N x C x V, V = A x t, e = a x N where n = number of molecules, N = Avogadro's number, V = volume of cuvette, A = area of cuvette, t = thickness of cuvette, C = concentration of fluid in the cuvette, e = extinction coefficient, a = effective area of molecule. (a) By using calculus in dI = -I x a x N x C x dt, prove that ln (I / Io) = -a x N x C x t, where dI is the small difference in I and dt is the small difference in t. I = intensity of light. Io = initial intensity of light. (b) Show by calculations that ln (Io / I) = e x C x t based on the answer in the previous question (a). (c) Find the equation of log (Io / I) as a function of e, C and t based on the answer in the previous question (b).
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CHEMICAL ENERGY BALANCE - EXAMPLE 11.2 : Calculate the cooling duty, H required to condense and cool acetone from 100 degree Celsius to 25 degree Celsius at atmospheric pressure. The heat of vaporization for acetone at its normal boiling point is 30.2 kJ / mol. The boiling point of acetone at atmospheric pressure is 56 degree Celsius. The flowrate of acetone through the condenser is 100 mol / s = N. Value of sensible heat needed to increase the temperature of acetone in liquid form from 25 to 56 degree Celsius is 4.06 kJ / mol. Value of sensible heat needed to increase the temperature of acetone in vapor form from 56 to 100 degree Celsius is 3.82 kJ / mol. Unit of H is kJ / s.
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Chemical Engineering Energy Balance - Please match the term A - E as follow with the stated definition : A. Yield. B. Selectivity. C. Relative saturation. D. Molal saturation. E. Absolute saturation. i. Answer : ? (moles of desired product formed) / (moles that would have been formed if there were no side reactions and the limiting reactant has reacted completely). ii. Answer : ? (moles of desired product formed) / (moles of undesired product formed). iii. Answer : ? (relative humidity 40 % means partial pressure of water vapour equals 4 / 10 of the vapour pressure of water at the system temperature). iv. Answer : ? (moles of vapour) / (moles of vapour dry gas). v. Answer : ? (mass of vapour) / (mass of dry gas).
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