Comminution theories — identify Bond’s law:\nWhich statement correctly characterises Bond’s crushing law in size reduction?

Introduction / Context:
Comminution (crushing and grinding) power requirements are estimated using empirical laws: Kick’s law, Rittinger’s law, and Bond’s law. Each relates specific energy to a function of the size reduction ratio and is valid over a certain size range. Bond’s “third theory of comminution” is widely used for design correlations in crushing and milling circuits.

Given Data / Assumptions:

• Feed is very large relative to product (the classic Bond simplification).
• Characteristic size is represented by a screen size such as 80% passing (F80, P80).

Concept / Approach:
Bond’s law states that the specific energy E is proportional to (1/√P) − (1/√F), where F and P are characteristic feed and product sizes. For very large feed (F → ∞), 1/√F → 0, so E ∝ 1/√P. In contrast, Rittinger’s law states E ∝ (1/P − 1/F), corresponding to new surface creation and exaggerating energy for very fine sizes; Kick’s law uses a logarithmic size ratio for coarse crushing. Thus the statement linking energy to the inverse square root of product size aligns with Bond’s law.

Step-by-Step Solution:

Verification / Alternative check:
Design handbooks use Bond work index W_i with E = W_i * (10/√P − 10/√F) for P, F in micrometres, reinforcing the inverse-square-root size dependence.

Why Other Options Are Wrong:

• New surface proportionality (option d) is Rittinger’s law, not Bond’s.
• Independence from size (option e) contradicts all comminution theories.
• Option a’s comparison wording is ambiguous; Bond predicts less severe energy rise than Rittinger for very fine sizes but does not “call for” fine energy generically.
• Option b is too sweeping; Bond is widely applied in practice.

Common Pitfalls:
Confusing the three laws’ size ranges; Bond is intermediate between Kick and Rittinger.

Final Answer:
It states that energy required from very large feed is proportional to 1/sqrt(product size).