BIOCHEMICAL ENGINEERING INSTRUMENTATION - EXAMPLE 29.1 : In the application of Theory of Spectrometry in spectrophotometer, let n = N x C x V, V = A x t, e = a x N where n = number of molecules, N = Avogadro's number, V = volume of cuvette, A = area of cuvette, t = thickness of cuvette, C = concentration of fluid in the cuvette, e = extinction coefficient, a = effective area of molecule. (a) By using calculus in dI = -I x a x N x C x dt, prove that ln (I / Io) = -a x N x C x t, where dI is the small difference in I and dt is the small difference in t. I = intensity of light. Io = initial intensity of light. (b) Show by calculations that ln (Io / I) = e x C x t based on the answer in the previous question (a). (c) Find the equation of log (Io / I) as a function of e, C and t based on the answer in the previous question (b).
BIOCHEMICAL ENGINEERING INSTRUMENTATION - ANSWER 29.1 : (a) Let dI = -I x a x N x C x dt, then dI / I = -a x N x C x dt. Integrate both sides of the equation gives ln (I / Io) = -a x N x C x t. (b) When ln (I / Io) = -a x N x C x t and e = a x N, then ln (I / Io) = -e x C x t. If ln (I / Io) = - ln (Io / I), then ln (Io / I) = e x C x t. (c) Let ln (Io / I) = log (Io / I) / log E, where E = 2.718 approximately. Then log (Io / I) = log E x ln (Io / I) = log E x e x C x t. 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 PHYSICS - EXAMPLE 30.1 : Two viruses a and b with masses of Ma and Mb are moving at velocities of Va and Vb respectively, facing towards each other and collide. After collision both masses of Ma and Mb disappear. (a) Find the total momentum available for both a and b. Hint : momentum = mass x velocity = M x V. (b) Guess the total energy E generated from the disappearance of a and b. Let c to be the velocity of light. Hint : E is equal to M c square.
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