Bond work index (Wi): choose the correct definition used for comparative comminution energy in design and scale-up.

Introduction / Context:
The Bond work index (Wi) is a material constant used in mill power calculations. It normalizes grindability by defining a comparative energy to reach a standard product size from an infinitely large feed size, enabling equipment selection and scale-up.

Given Data / Assumptions:

• Standard product size: 80% passing 100 microns (P80 = 100 μm).
• Reference from “infinite” or very large feed size (F80 → ∞).
• Energy basis: kWh per ton.

Concept / Approach:
Bond’s equation relates specific energy E to size as E = Wi * (10/√P80 − 10/√F80) with sizes in microns. For Wi’s definition, F80 approaches infinity so the second term vanishes, and Wi equals the energy to reach P80 = 100 μm from a very large feed.

Step-by-Step Solution:
Recall Wi definition: comparative grindability metric at P80 = 100 μm from large feed.Map to options: only option (a) matches this definition precisely.

Verification / Alternative check:
Bond grindability tests (ball mill Wi) produce Wi values used widely for SAG/ball mill sizing via empirical models.

Why Other Options Are Wrong:
(b), (d): specify single target sizes without the 80% passing criterion and ignore “infinite” feed basis.(c): wrong screen and ambiguous feed basis.

Common Pitfalls:
Confusing Wi with operating kWh/t for a specific circuit; Wi is a comparative property, not the actual circuit energy.

Final Answer:
Gross energy (kWh/ton of feed) needed to reduce very large feed to such a size that 80% of the product passes through a 100 micron screen.