Jaw crushing energy: during size reduction in a jaw crusher, the specific energy consumed does not systematically decrease with any listed operating change. Which statement best reflects this fact?

Introduction / Context:
Understanding how energy consumption behaves in primary crushers (like jaw crushers) is fundamental to equipment selection and process optimization. Classical comminution laws (Kick, Bond, Rittinger) relate specific energy to the size reduction ratio rather than absolute feed or product sizes alone. This question probes whether any of the listed changes guarantee a decrease in energy usage.

Given Data / Assumptions:

• Machine: jaw crusher operating at steady state.
• Energy considered on a per-unit-mass (specific) basis.
• Reduction ratio and material characteristics are the dominant factors in energy demand.

Concept / Approach:
Kick’s law: E/m ∝ ln(d_feed/d_product), emphasizing reduction ratio. Bond’s law: E/m ∝ (1/√d_product − 1/√d_feed). Rittinger’s law: E/m ∝ (1/d_product − 1/d_feed). All tie energy primarily to the size reduction accomplished, not simply feed size, product size, or capacity alone. Therefore, without changing reduction ratio or PSD targets, none of the listed adjustments consistently reduce energy.

Step-by-Step Solution:
Examine (a): decreasing product size raises reduction ratio; specific energy rises, not decreases.Examine (b): lowering capacity does not guarantee lower specific energy; often increases kWh/t due to less efficient loading.Examine (c): increasing feed size at constant reduction ratio keeps d_feed/d_product constant; specific energy remains similar, not necessarily lower.Conclusion: no option ensures a decrease → choose “none of these.”

Verification / Alternative check:
Plant data typically show kWh/t correlates with reduction ratio and work index. Variations in capacity or absolute sizes without altering the ratio do not provide a guaranteed energy decrease.

Why Other Options Are Wrong:
(a) Smaller product = higher energy demand.(b) Capacity changes affect throughput, not the fundamental energy per ton trend.(c) Constant reduction ratio implies similar specific energy demand.

Common Pitfalls:
Confusing absolute size with size reduction ratio; energy scales with the reduction accomplished, not capacity alone.

Final Answer:
none of these.