Question 99 - (a) The quantum number m is given by m = -s, -s + 1. If s = 0.5, find the values of m. (b) | T > = (cos T) | V > + (sin T) | H >. The V and H states form a basis for all polarizations. Let cos T = 0.8. (i) If (sin T)(sin T) + (cos T)(cos T) = 1, find the value of sin T. (ii) For | T > = a | V > + b | H >, where a x a represents the probability of | V > and b x b represents the probability of | H >. Which one is more abundant, | V > or | H >? (iii) Find the value of T without using any mathematical tools.
Answer 99 - (a) When s = 0.5, m = -s = -0.5 and m = -s + 1 = -0.5 + 1 = 0.5. (b)(i)(sin T)(sin T) = 1 - (cos T)(cos T) = 1 - 0.8 x 0.8 = 0.36. Then sin T = 0.6. (ii) Let a = cos T = 0.8, probability of | V > = a x a = 0.8 x 0.8 = 0.64 (more abundant) and b = sin T = 0.6, probability of | H > = b x b = 0.6 x 0.6 = 0.36 (less abundant). (iii) cos T = 0.8, then T = arc cos 0.8. 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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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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