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: The three primary empirical laws of comminution (size reduction) correlate energy input (E) with particle size change, from initial diameter (d$_1$) to final diameter (d$_2$).Rittinger's Law (1867): The energy needed is directly proportional to the new surface area generated. This law is best suited for fine grinding applications.\[ E \propto \left( \frac{1}{d_2} - \frac{1}{d_1} \right) \]Kick's Law (1885): The energy requirement is proportional to the logarithm of the reduction ratio. It's most appropriate for coarse crushing of larger particles.\[ E \propto \log \left( \frac{d_1}{d_2} \right) \]Bond's Law (1952): The energy needed scales proportionally with the created crack length. This law is the most commonly used for crushing and grinding in general.\[ E \propto \left( \frac{1}{\sqrt{d_2}} - \frac{1}{\sqrt{d_1}} \right) \]Given the question's focus on the logarithmic relationship, Kick's Law is the relevant one.