The sieve analysis of a finely ground rice powder is represented by a straight line from zero percent mass at 1 μm particle size to 100 percent mass at 101 μm particle size. The volume-surface mean diameter in μm is
Options:
(A) 14.6
(B) 19.2
(C) 21.7
(D) 25.3
Official Answer Key:
C
Step-by-Step Solution & Explanation
A straight-line cumulative mass distribution from D=1 μm (0%) to D=101 μm (100%) means the mass fraction is uniformly distributed over the size range, f(D) = 1/100 per μm for D ∈ [1,101]. The volume-surface (Sauter) mean diameter is defined as D_vs = 1 / ∫[f(D)/D]dD, integrated over the distribution. Evaluating ∫₁¹⁰¹ (1/100)/D dD = (1/100)ln(101/1) = (1/100)(4.615) = 0.04615, so D_vs = 1/0.04615 = 21.67 ≈ 21.7 μm, matching option (C).
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