Question

Energy required to grind a food material from one size to another is expressed by _________.
(A). Fick's law
(B). Kick's law
(C). Rittinger's law
(D). Bond's law
Choose the correct answer from the options given below:

• A. (A), (C) and (D) only.
• B. (A), (B) and (D) only.
• C. (A), (B) and (C) only.
• D. (B), (C) and (D) only.

Hint:

To remember the three grinding laws, use the acronym "KBR" (Kick, Bond, Rittinger), representing exponents \(n = 1\), \(1.5\), and \(2\) in the energy equation, respectively.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Size reduction (grinding, milling, or crushing) is a common unit operation in food processing used to reduce solid foods to smaller particle sizes.
The process is energy-intensive, and several semi-empirical laws are used to estimate the energy required based on the initial and fil particle sizes.
Key Formula or Approach:
The general differential equation for size reduction is expressed as:
\[ \frac{dE}{dx} = -C \cdot x^{-n} \]
where \(dE\) is the energy required, \(dx\) is the change in particle size, \(C\) is a constant, and \(n\) is an exponent that varies depending on the law applied.

Step 2: Detailed Explation:
The three classical laws derived from this general equation are:
- Kick's Law (\(n = 1\)): Assumes the energy required for size reduction is proportiol to the reduction ratio (\(\ln(x_1/x_2)\)).
It is most accurate for coarse grinding of large, ductile particles.
This matches with statement (B).
- Rittinger's Law (\(n = 2\)): Assumes the energy required is proportiol to the new surface area created during grinding.
It is most accurate for fine grinding of brittle materials.
This matches with statement (C).
- Bond's Law (\(n = 1.5\)): Assumes the energy required is inversely proportiol to the square root of the particle size.
It is used for intermediate size reduction ranges.
This matches with statement (D).
- Fick's Law (A) describes the molecular diffusion of mass down a concentration gradient, which is unrelated to mechanical grinding or size reduction.
Therefore, only Kick's, Rittinger's, and Bond's laws are used to express grinding energy.

Step 3: Fil Answer:
The grinding energy laws are Kick's, Rittinger's, and Bond's laws, which correspond to (B), (C), and (D).
Hence, the correct option is (D).