Question

Comminution energy requirement is quantitatively estimated using:

• A. Stokes' law
• B. Raoult's law
• C. Darcy's law
• D. Bond's law

Hint:

Remember the three classical comminution theories: von Rittinger's (energy proportional to new surface area), Kick's (energy proportional to volume reduction ratio), and Bond's (energy proportional to crack length, suitable for intermediate grinding sizes).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the empirical law used to quantitatively estimate the energy required for comminution processes.
Comminution is the mechanical process of reducing the particle size of ores through crushing and grinding, which is the first step in mineral processing.

Step 2: Key Formula or Approach:
The general differential equation for comminution energy states:
\[ dE = -C \frac{dX}{X^f} \]
where \( E \) is energy, \( X \) is particle size, and \( C \) and \( f \) are constants.
For Bond's Law, the value of the exponent \( f \) is chosen as \( 1.5 \). Integration yields:
\[ E = 10 \cdot W_i \left( \frac{1}{\sqrt{P_{80}}} - \frac{1}{\sqrt{F_{80}}} \right) \]
where:
\( E \) is the specific energy input (kWh/ton),
\( W_i \) is the Bond Work Index of the material,
\( F_{80} \) is the feed size at which \( 80\% \) of particles pass, and
\( P_{80} \) is the product size at which \( 80\% \) of particles pass.

Step 3: Detailed Explanation:

• Bond's Third Theory of Comminution: Bond's law states that the work useful in cracking is directly proportional to the length of new cracks formed.
Since crack length is proportional to the square root of the new surface area created, the energy required is inversely proportional to the square root of the product particle size.
It is widely used in the mining industry for sizing industrial crushers and tumbling mills.

• Comparison with Other Options:
-

Stokes' law (Option A) determines the settling velocity of spherical particles in a viscous fluid, which is relevant to classification but not size reduction energy.
-

Raoult's law (Option B) describes the vapor pressure of ideal thermodynamic solutions.
-

Darcy's law (Option C) describes the flow of fluid through a porous medium.


Step 4: Final Answer:
Thus, the comminution energy requirement is quantitatively estimated using Bond's law, which is Option (D).