Bond’s work index: what are the dimensions/units of the work index used in Bond’s crushing and grinding equation?

Introduction / Context:
Bond’s equation relates the energy required for size reduction to the 80% passing sizes of feed and product. The proportionality factor is the work index, a material property used in mill selection and power estimation.

Given Data / Assumptions:

• Conventional SI/industrial practice.
• Focus is on units associated with the work index.

Concept / Approach:
Bond’s work index, Wi, is defined as the energy per unit mass required to reduce a very large feed to a size such that 80% passes 100 micrometres (in the standard test), expressed in kilowatt-hours per metric ton.

Step-by-Step Solution:
Recall definition: energy per mass → kWh/ton.Check dimensionality: energy (kWh) divided by mass (ton) → consistent with power–time per mass.Select kWh/ton.

Verification / Alternative check:
Bond grindability tests report Wi values (e.g., 8–20 kWh/ton) in tabulations for ores.

Why Other Options Are Wrong:
Dimensionless: false—Wi has energy per mass units.kW/ton: power per mass; not the definition.kWh·m^1/2/ton: a misinterpretation of the size terms in the equation.

Common Pitfalls:
Confusing the units of Wi with the slope/intercept units from linearized plotting methods.

Final Answer:
kWh/ton