For estimating the work required to grind coal to minus 200 mesh in a ball mill, which comminution law is considered most accurate over this size range?

Introduction / Context:
Different energy–size relationships are applied depending on size range and mechanism. For ball milling from coarse to moderately fine sizes, Bond’s law is widely adopted for engineering estimates.

Given Data / Assumptions:

• Target size: minus 200 mesh (≈ 74 microm).
• Equipment: ball mill.
• Material: coal (typical Bond work index available).

Concept / Approach:
Kick’s law suits coarse crushing where size ratios matter; Rittinger’s law suits very fine grinding dominated by new surface creation. Bond’s law bridges these regimes and is empirically correlated with mill performance through the Bond work index, making it the practical choice for ball mill power estimates around 100–75 microm.

Step-by-Step Solution:
Identify size range: intermediate-to-fine (ball milling domain).Select law with best empirical support: Bond.Answer: Bond’s law.

Verification / Alternative check:
Design handbooks use Bond equation with W_i for ball mill sizing to 200 mesh.

Why Other Options Are Wrong:
Rittinger: too fine-focused; may overpredict in this range.Kick: coarse-size focused; underpredicts for fine grinding.No law: Bond is well established.

Common Pitfalls:
Applying Rittinger universally to all fine grinding; empirical validation favours Bond here.

Final Answer:
Bond’s law