Question

The energy required for size reduction is proportional to the logarithm of size reduction ratio, is given by  law.

• A. Kicks' Law
• B. Bonds' Law
• C. Ricks' Law
• D. Rittingers' Law

Hint:

Remember the three laws by their mathematical form: \textbf{Rittinger} (1/d), \textbf{Kick} (log d), \textbf{Bond} ($\frac{1}{\sqrt{d}}$). Kick's law applies to coarse 'kicking' or crushing.

Answer 1

The Correct Option is A

Step 1: Recall the three main empirical laws of comminution (size reduction). These laws relate the energy input (E) to the change in particle size from an initial diameter (d$_1$) to a final diameter (d$_2$). Rittinger's Law (1867): States that the energy required is proportional to the new surface area created. It is most applicable to fine grinding. \[ E \propto \left( \frac{1}{d_2} - \frac{1}{d_1} \right) \] Kick's Law (1885): States that the energy required is proportional to the logarithm of the reduction ratio. It is most applicable to coarse crushing of large particles. \[ E \propto \log \left( \frac{d_1}{d_2} \right) \] Bond's Law (1952): States that the energy required is proportional to the crack length produced, and it is the most widely used law for general crushing and grinding. \[ E \propto \left( \frac{1}{\sqrt{d_2}} - \frac{1}{\sqrt{d_1}} \right) \] The question specifically asks for the law involving the logarithm, which is Kick's Law.