Comminution energetics: under otherwise comparable conditions, energy consumption per unit mass in a crusher decreases with an increase in which of the following?

Introduction / Context:
Power and energy in size reduction operations are governed by empirical laws (Kick, Bond, Rittinger) and equipment characteristics. Understanding how energy per unit mass shifts with product size, feed size, and machine capacity helps in selecting stages and predicting costs.

Given Data / Assumptions:

• Similar ore and operating conditions.
• Comparison is on specific energy (kWh/ton), not absolute power.
• Reduction ratio effects are considered where stated.

Concept / Approach:
For a fixed feed size, making a coarser product (larger product size) requires less new surface area, hence less energy (Rittinger emphasizes surface creation). At constant reduction ratio, increasing feed size generally favors Kick’s law, indicating energy proportional to the size ratio log, making specific energy less sensitive and often lower per ton at larger absolute sizes. Higher-capacity machines tend to have better mechanical efficiency and lower specific energy because of scale effects and reduced idle/overhead losses per unit throughput.

Step-by-Step Solution:
Option (a): Coarser product → less surface area created → lower energy per ton.Option (b): Larger machines/throughputs → better utilization → lower kWh/ton.Option (c): At constant reduction ratio, larger absolute feed sizes generally reduce specific energy (Kick regime) compared with fine grinding (Rittinger regime).Therefore, (d) all three are valid trends.

Verification / Alternative check:
Plant data commonly show higher kWh/ton in fine crushing and grinding steps than in primary/secondary stages, reflecting increased surface area creation demands.

Why Other Options Are Wrong:
Choosing only one factor understates the multi-parameter nature of comminution energetics; all listed factors contribute to lower specific energy.

Common Pitfalls:
Confusing installed motor power (kW) with specific energy (kWh/ton); larger machines may draw more kW but process far more tons, reducing kWh/ton.

Final Answer:
all (a), (b) & (c)