Comminution laws — identify Rittinger’s law:\nWhich expression represents Rittinger’s crushing (grinding) law for specific energy in terms of characteristic feed and product sizes?

Introduction / Context:
Three classical energy–size relations guide comminution analysis: Kick’s, Bond’s, and Rittinger’s laws. Each associates specific energy with a different function of the feed and product sizes and applies best in a particular size range. Rittinger’s law emphasises surface creation and is most applicable at fine sizes where new surface area dominates the energy requirement.

Given Data / Assumptions:

• P/m is specific power (energy per mass rate).
• Df and Dp denote characteristic feed and product sizes, respectively.

Concept / Approach:
Rittinger’s law states that specific energy is proportional to new surface area produced, which for similar particle shapes scales with (1/Dp − 1/Df). Kick’s law relates energy to the natural logarithm of the size ratio ln(Df/Dp), suitable for coarse crushing. Bond’s law uses the inverse square-root term (1/√Dp − 1/√Df), widely applied in grinding mill design. Therefore, the correct expression for Rittinger is P/m = K * (1/Dp − 1/Df).

Step-by-Step Solution:

Verification / Alternative check:
Textbook derivations equate energy to surface created with proportionality K, yielding the 1/D form; Bond’s and Kick’s distinct forms help cross-check.

Why Other Options Are Wrong:

• ln(Df/Dp): Kick’s law (coarse range).
• (1/√Dp − 1/√Df): Bond’s law (intermediate range).
• Independence from size ratio: contradicts all three laws.

Common Pitfalls:
Forgetting which exponent belongs to which law; use the mnemonic Rittinger (1/D), Bond (1/√D), Kick (ln D).

Final Answer:
P/m = K * (1/Dp − 1/Df)