Question 108 - (a) The correct statement about both the average value of position (<x>) and momentum (<p>) of a 1-dimensional harmonic oscillator wavefunction is <x> = <p> = 1 - x. Find the value of x. (b) The probabilities of finding a particle around points A, B and C in the wavefunction y = f(x) are P(A), P(B) and P(C) respectively. Coordinates are A (3,5), B (4,-10) and C (6,7). Arrange P(A), P(B) and P(C) in term of a < b < c, when | y-coordinate | signifies the probability.
Answer 108 - (a) Let <x> = <p> = 1 - x = 0, then x = 1 - 0 = 1. (b) With reference to the | y-coordinate | for each point in A, B and C coordinates, if 5 < 7 < |-10| then a < b < c = P(A) < P(C) < P(B). 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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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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Three solid objects of the same material and of equal mass – a sphere, a cylinder (length = diameter) and a cube – are at 5000C initially. These are dropped in a quenching bath containing a large volume of cooling oil each attaining the bath temperature eventually. The time required for 90% change of temperature is smallest for a) cube b) cylinder c) sphere d) equal for all the three whyyyyyyy???????
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Question 78 - Fact 1 : Dry air contains 20.95 % oxygen, 78.09 % nitrogen, 0.93 % argon, 0.039% carbon dioxide, and small amounts of other gases by volume. Fact 2 : Volume occupied is directly proportional to the number of moles for ideal gases at constant temperature and pressure. Fact 3 : 12.5 moles of pure oxygen is required to completely burn 1 mole of pure octane. Fact 4 : Air–fuel ratio (AFR) is the mass ratio of dry air to fuel present in a combustion process such as in an internal combustion engine or industrial furnace. Fact 5 : Molecular weight of oxygen gas is 31.998 g / mole and molecular weight of nitrogen gas is 28.014 g / mole. (a) Find the molar ratio of nitrogen and oxygen, or (moles of nitrogen) / (moles of oxygen) in dry air, by assuming ideal features of nitrogen and oxygen gases. (b) How many moles of nitrogen are available if dry air is used to completely burn the 1 mole pure octane? (c) Find the mass of fuel of 1 mole of octane with molecular weight of 114.232 g / mole. (d) Find the mass of dry air with 12.5 moles of pure oxygen by assuming only oxygen and nitrogen gases exist in the air. (e) Find the air-fuel ratio (AFR) when octane is used as fuel. (f) Find the fuel-air ratio (FAR) when octane is used as fuel.
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