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.
ENGINEERING MATHEMATICS - ANSWER 8.4 : Rearranging the equation gives P v^3 - (Pb + RT) v^2 - av + ab = 0. By using Excel program of computer v = 0.19322. Solver : FILE -> Options -> Add-Ins -> Solver Add-in. Goal seek : DATA -> What-If-Analysis -> Goal Seek. In both functions, Set cell / Objective, To value / Value Of, By changing cell / Changing Variable Cells should be used where To value / Value Of = 0, By changing cell / Change Variable Cells is the assumed v value, Set cell / Objective is the equation of function. 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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ENGINEERING NUMERICAL METHODS - EXAMPLE 19.1 : Solve the simultaneous equation using simple Excel program : r + s - t = 7, 2r - s = 0, 3r + 2t = 15. Explain the use of functions of MINVERSE and MMULT together with the keyboard C (Ctrl) + S (Shift) + E (Enter).
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X is strong but has a very low density (1% of traditional earth materials.) and hence light weight. It is a recyclable material. The compression behaviour of X is strain rate dependent. Higher strain rates result in higher initial modulus and higher compression strength. It can also withstand unlimited number of cycling loading provided the repetitive loads are kept below 80% of the compressive strength. The internal structure of the material includes air-traps which make it poor heat conductor. X is non- biodegradable and chemically inert in both soil and water. Most acids and their water solutions do not attack it; however strong oxidizing acids do. Solvents which attack X include esters, ketones, ethers, aromatic and aliphatic hydrocarbons and their emulsions, among others. It does not support bacterial/fungal growth as well .It also has significant acoustic properties and effectively reduces the transmission of airborne sound. X is combustible and should not be exposed to open flame or other ignition sources. Combustion products are carbon monoxide, carbon dioxide, water and soot. Long-term exposure to sunlight causes yellowing and a slight embrittlement of the surface due to ultraviolet light. X is able to withstand the rigours of temperature cycling, assuring long-term performance.
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QUANTUM BIOLOGY - EXAMPLE 33.5 : (a) In the measurement of the number of photons received by a plant during photosynthesis, quantum meter is used. At 8 AM, 11 AM, 12 PM, 2 PM and 4 PM of the same day, the measured readings of the meter are 10, 70, 60, 120 and 120 units. Find the mode, median and min of the readings of the quantum meter. (b) Microtubule is used to carry information in a cell. If the cross-sectional area of the microtubule has a diameter of 25 nanometers, find the volume of the microtubule of 1 nanometer in height. State the assumption of calculation.
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