Subtopic: Particle size analysis for comminuted solids
Question Statement:
In a particle size analysis, the following results are obtained:
| Mass of particles (g) | 2 | 5 | 7 | 4 | 1 |
|---|---|---|---|---|---|
| Mean size of particles (µm) | 350 | 240 | 200 | 150 | 100 |
The volume-surface mean diameter of the particles in µm is ______
Official Answer Key:
192.5 to 193.5
Step-by-Step Solution & Explanation
The volume-surface (Sauter) mean diameter is defined as D_vs = Σm_i / Σ(m_i/d_i), i.e. total mass divided by the sum of (mass/diameter) for each size class, since mass is proportional to volume for particles of similar density. Σm_i = 2+5+7+4+1 = 19 g. Σ(m_i/d_i) = 2/350+5/240+7/200+4/150+1/100 = 0.00571+0.02083+0.035+0.02667+0.01 = 0.09821. D_vs = 19/0.09821 = 193.5 µm, within the accepted band 192.5–193.5.
Section 7 — Dairy and Food Engineering
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.