QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.2 : (a) Let | - > = 1 | x > + 0 | y >, | | > = 0 | x > + 1 | y >. Find the value of 2 | x > + 3 | y > in term of | - > and | | >. (b) Let m to be the reduced mass. Find the value of m in term of Ma and Mb where 1 / m = 1 / Ma + 1 / Mb.
QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - ANSWER 31.2 : (a) For | - > = 1 | x > + 0 | y >, multiply it with 2 to produce 2 | - > = 2 | x > + 0 | y >, then 2 | x > = 2 | - > - 0 | y > as first equation. For | | > = 0 | x > + 1 | y >, multiply it with 3 to produce 3 | | > = 0 | x > + 3 | y >, then 3 | y > = 3 | | > - 0 | x > as second equation. Finally first equation plus second equation to produce 2 | x > + 3 | y > = 2 | - > + 3 | | >. (b) Let 1 / m = 1 / Ma + 1 / Mb = (Ma + Mb) / (Ma x Mb). Then m = (Ma x Mb) / (Ma + Mb). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; email@example.com; http://kangchuentat.wordpress.com.
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MASS TRANSFER - EXAMPLE 4.1 : A concentric, counter-current heat exchanger is used to cool lubricating oil. Water is used as the coolant. The mass flow rate of oil into the heat exchanger is 0.1 kg / s = FO. For oil, the inlet temperature TIO = 100 degree Celsius and the outlet temperature TOO = 55 degree Celsius. For water, the inlet temperature TIW = 35 degree Celsius and the outlet temperature TOW = 42 degree Celsius. What is the mass flow rate of water in kg / s, FW needed to maintain these operating conditions? Constant for heat capacity of oil is CO = 2131 J /(kg K) and for water is CW = 4178 J /(kg K). Use the equation (FO)(CO)(TIO ?TOO) = (FW)(CW)(TOW ?TIW).
ENGINEERING MECHANIC - EXAMPLE 15.2 : A cantilever beam of length L = 3 m carries a uniformly distributed load (UDL) of W = 20 N / m throughout the length. Calculate the bending moment, BM of the beam near the fixed end. What is the shear force, SF at this point? Let SF = -WL, BM = -LWL/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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The water is superheated steam at 440 degree Celsius and 17.32 megapascals. Estimate the enthalpy of the steam above. From the steam table for water at 440 degree Celsius, enthalpy of steam, h at 18 megapascals is 3103.7 kilojoules per kilogram and at 16 megapascal is 3062.8 kilojoules per kilogram. Assume that h = mP c where P is pressure; m and c are constants at fixed temperature with small differences in P.
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Question 109 - (a) Acceptable wavefunction in quantum mechanics in the range of : negative infinity < x < positive infinity, vanishes at least at one boundary. Which of the following is the wavefunction or are the wavefunctions of acceptable theory : P = x, P = | x |, P = sin x, P = exp (-x), P = exp (-| x |)? State the reason. (b) Let linear momentum operator P = -ih d / dz. The wavefunction is S = exp (-ikz) where i x i = -1, k and h are constants. Find the linear momentum of such wavefunction by using the term P x S.
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POLYMER ENGINEERING - QUESTION 24.3 : The molecular weights M in kg / mol of 3 different monomers a, b and c in a polymer are Ma = 14, Mb = 16 and Mc = 18, with their respective quantities in N units having the ratio of Na : Nb : Nc = 2 : 3 : 5. (a) Find the numerical average molecular weight of the polymer by using the formula (Ma Na + Mb Nb + Mc Nc) / (Na + Nb + Nc). (b) Find the weighted average molecular weight of the polymer by using the formula (Ma Na Ma + Mb Nb Mb + Mc Nc Mc) / (Ma Na + Mb Nb + Mc Nc). (c) Calculate the polydispersity Q by using the answer in (b) divided by answer in (a). (d) Find the volumetric average molecular weight of the polymer by using the formula (Ma Na Ma Ma + Mb Nb Mb Mb + Mc Nc Mc Mc) / (Ma Na Ma + Mb Nb Mb + Mc Nc Mc). (e) Estimate the polydispersity Q by using the answer in (d) divided by answer in (b).
ENGINEERING DRAWING - EXAMPLE 18.3 : Autocad computer program is used to draw a pipe that is used to transport natural gases for processing. Actual length of the pipe is 10 metres. The pipe has cross sectional area of circle in shape with measured circumference of s = 3 metres. (a) If 10 units are used to represent the actual length of the pipe in computerised engineering drawing, find the diameter of the pipe, d that will be shown in the engineering drawing. (b) If one unit in the program equals to 1 centimetre, find the scale used in the computer program.
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