Question

The given equation represents which law: \[ E = K_k \ln \frac{d_1}{d_2} \]

• A. Rittinger’s law
• B. Bond’s law
• C. Fick's law
• D. Kick’s law

Hint:

Kick’s law is used for coarse grinding, assuming that energy required is proportional to the logarithm of size reduction ratio.

Answer 1

The Correct Option is D

Step 1: Understanding the given equation. The given equation: \[ E = K_k \ln \frac{d_1}{d_2} \] relates energy (\( E \)) to the size reduction of particles (\( d_1 \) and \( d_2 \)). This equation is derived from Kick’s law, which states that the energy required for size reduction is proportional to the logarithm of the ratio of initial to final particle sizes. 

Step 2: Explanation of Kick’s Law. Kick’s law is expressed as: \[ E = K_k \ln \frac{d_1}{d_2} \] where: 
- \( E \) = Energy required for size reduction, 
- \( K_k \) = Kick’s constant, 
- \( d_1 \) and \( d_2 \) = Initial and final particle sizes. 

Step 3: Why other options are incorrect.
 - (A) Rittinger’s law: States that energy required is proportional to the new surface area created, using \( E = K_R \left( \frac{1}{d_2} - \frac{1}{d_1} \right) \). 
- (B) Bond’s law: Uses an empirical equation to calculate energy consumption in size reduction. 
- (C) Fick's law: Describes diffusion, unrelated to particle size reduction.