Question

The ``power required is proportional to the square root of the product size'' is ______

• A. Kick's law
• B. Bond's law
• C. Rittinger's law
• D. Work index

Hint:

A simple way to remember the exponents in the differential equation \( dE \propto -dD_p / D_p^n \):
Kick's Law: \( n = 1 \)
Bond's Law: \( n = 1.5 \)
Rittinger's Law: \( n = 2 \)
These are sorted alphabetically: K (1), B (1.5), R (2).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks us to identify the specific size-reduction law that states the energy/power required is proportional to the reciprocal of the square root of the product size.
This is a core topic in size reduction under mechanical operations.

Step 2: Key Formula or Approach:
The general differential equation for size reduction is given by Walker's Law:
\[ dE = -C \cdot \frac{dD_p}{D_p^n} \]
where different values of the exponent \( n \) lead to the three classical laws of size reduction: Rittinger's, Kick's, and Bond's laws.

Step 3: Detailed Explanation:

• Bond's Law (\( n = 1.5 \)): Integrating the differential equation for \( n = 1.5 \) yields:
\[ E = 2 \cdot C \cdot \left( \frac{1}{\sqrt{D_{p2}}} - \frac{1}{\sqrt{D_{p1}}} \right) \]
where \( D_{p2} \) is the product size and \( D_{p1} \) is the feed size.
For cases where feed size is large, the energy is inversely proportional to the square root of the product size:
\[ E \propto \frac{1}{\sqrt{D_{p2}}} \]
This is the physical statement of Bond's Law.

• Rittinger's Law (\( n = 2.0 \)): The energy required is proportional to the new surface area created:
\[ E \propto \left( \frac{1}{D_{p2}} - \frac{1}{D_{p1}} \right) \]

• Kick's Law (\( n = 1.0 \)): The energy required is proportional to the ratio of initial to final size:
\[ E \propto \ln\left(\frac{D_{p1}}{D_{p2}}\right) \]

• Work Index: This is a parameter used in Bond's law representing the energy required to reduce unit mass of material from infinite size to 100 microns.


Step 4: Final Answer:
The statement describes Bond's law of size reduction.