Question

_____ state’s that the grinding energy for a given mass of material is proportional to the logarithm of reduction ratio.

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

Hint:

Associate the laws of size reduction with their mathematical indices: - Kick's Law $\rightarrow$ Logarithmic ratio ($\ln(D_1/D_2)$). - Rittinger's Law $\rightarrow$ New surface area ($1/D_2 - 1/D_1$). - Bond's Law $\rightarrow$ Square root of diameter ($1/\sqrt{D_2} - 1/\sqrt{D_1}$).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Size reduction is an important unit operation in food processing used to break down solids into smaller particles (e.g., grinding grains, milk powder, or spices).
Several classical laws describe the relationship between energy input and the change in particle size.

Step 2: Detailed Explanation:
Let us review the laws of size reduction:
- Kick's Law: States that the energy required to reduce a given mass of material is constant for a given ratio of size reduction, regardless of the initial particle size.
Mathematically, the energy ($E$) is proportional to the logarithm of the ratio of initial to final particle size (reduction ratio):
\[ E = C_K \ln\left(\frac{D_1}{D_2}\right) \]
Where $D_1$ is the feed size and $D_2$ is the product size.
- Rittinger's Law: States that the energy required for size reduction is directly proportional to the new surface area created. This applies primarily to fine grinding.
- Bond's Law: States that the energy required is inversely proportional to the square root of the product particle diameter, which is useful for medium-to-coarse grinding.
Therefore, Kick's law is the principle stating that grinding energy is proportional to the logarithm of the reduction ratio.

Step 3: Final Answer
The correct option is (A).