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Mechanical Operations - Engineering

Q1:

__________ is defined as the geometric mean of the relative rejections and the relative recoveries of two minerals.

A Separation efficiency

B Selectivity index

C Concentration ratio

D none of these

ANS:B - Selectivity index

The term selectivity index is defined as the geometric mean of the relative rejections and the relative recoveries of two minerals.

Explanation:

  • Selectivity Index: In mineral processing and ore beneficiation, the selectivity index is a measure used to assess the effectiveness of a separation process in selectively concentrating one mineral over another. It is defined mathematically as the geometric mean of the relative rejections and the relative recoveries of the minerals.
  • Relative Rejection: Refers to the fraction of a mineral rejected in the tailings relative to its initial concentration in the feed.
  • Relative Recovery: Refers to the fraction of a mineral recovered in the concentrate relative to its initial concentration in the feed.
  • Geometric Mean: The selectivity index SSS is expressed as: S=R1⋅R2S = \sqrt{R_1 \cdot R_2}S=R1​⋅R2​​ Where:
    • R1R_1R1​ is the relative rejection of mineral 1.
    • R2R_2R2​ is the relative rejection of mineral 2.
  • Significance: A higher selectivity index indicates better separation efficiency in concentrating one mineral while rejecting the other, which is crucial in optimizing mineral processing operations for economic and environmental reasons.
Therefore, among the options provided, the selectivity index is specifically defined as the geometric mean of the relative rejections and the relative recoveries of two minerals in a separation process.