THERMODYNAMIC - EXAMPLE 10.2 : A cylinder with a movable piston contains 0.1 mole of a monoatomic ideal gas. The piston moves through state a, b and c. The heat Q, changes from state c to a is + 685 J. The work W, changes from state c to a is - 120 J. The work, W performed from state a to b then to c is 75 J. By using the first law of thermodynamic, U = Q + W where U is the internal energy : (a) Determine the change in internal energy between states a and c. (b) Is heat added or removed from the gas when the gas is taken along the path abc? (c) Calculate the heat added or removed when the gas is taken along the path abc?
THERMODYNAMIC - ANSWER 10.2 : (a) U = Q + W = 685 J - 120 J = 565 J. (b) For path a to c, U = - 565 J - heat is removed. (c) Q = U - W = - 565 J - 75 J = - 640 J (heat energy is removed when the value is negative). 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 48 - Let a ^ 2 = a x a and a ^ 3 = a x a x a where ^ is power function. Niobium is a metal with a body-centered cubic structure. The length of the unit cell structure is b = 0.3349 nm. (a) Find the volume for a unit cell structure for niobium. (b) There are 2 atoms per unit cell structure of niobium. The metal has a molar mass of 92.9 g / mol. One mole of the metal consists of 6.02 x 10 ^ 23 atoms. Find the mass of niobium per unit cell and the density of niobium.
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QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.9 : When an algebraic product is defined on the space, the Lie bracket is the commutator [x,y] = xy - yx according to Lie algebra in mathematics. If [p,x] f(x) = px f(x) - xp f(x), p = -ih d / dx, find the value of [p,x] in term of i and h.
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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.
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.37 : A biochemical engineering professional applies 5-step Du Pont formula in the accounting. Let Net Income = A, Earning Before Tax (EBT) = B, Earning Before Interest, Tax (EBIT) = C, Net Sales = D, Total Assets = E, Shareholders Equity = F. Let Tax Burden = A / B = 0.75, Interest Burden = B / C = 1.05, EBIT Margin = C / D = 0.27, Asset Turnover = D / E = 0.66, Return on Equity = A / F = 0.37. (a) Calculate the value of Leverage = E / F. (b) If AB + BC + CD + DE + EF = $$ 141932, find the values of A, B, C, D, E and F.
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