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HW3_2011_sol - Problem 1 Problem 2 a Based on steady state...

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Problem 1 Problem 2 a) Based on steady state cell mass balance, it can be shown that the dilution rate F/V (D) must equal specific growth rate (μ). Therefore, up to certain maximum D, incremental increase of D can increase specific growth rate of the culture leading to increase of the cell density. b) Since this is a substrate limited growth, at steady state, assume there is no substrate at output stream. Then, Y X/S = X / (0.05 × 180 – 0). By plotting 1/D vs 1/Y X/S , we can find Y TRUE at the Y-intercept. 1/Y X/S = m/D + 1/Y TRUE D (hr-1) X (g/L) Ideal Yx/s 1/D 1/Yx/S 0.05 1.58 2.86 0.175555556 20 5.696203 0.1 2.17 2.86 0.241111111 10 4.147465 0.15 2.47 2.86 0.274444444 6.666667 3.643725
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0.2 2.65 2.86 0.294444444 5 3.396226 0.25 2.76 2.86 0.306666667 4 3.26087 0.3 2.83 2.86 0.314444444 3.333333 3.180212 0.35 2.86 2.86 0.317777778 2.857143 3.146853 0.4 2.84 2.84 0.315555556 2.5 3.169014 0.45 2.74 2.74 0.304444444 2.222222 3.284672 0.5 2.25 2.25 0.25 2 4 0.52 1.32 1.32 0.146666667 1.923077 6.818182 0.53 0 0 0 1.886792 #DIV/0! Using the greyed area data points to plot, Then fit to linear eqn, Y TRUE = 1/2.647 = 0.378 (g cell/ g substrates)
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