Question

The work required for crushing a given material is proportional to the logarithm of the ratio between the initial and final diameters is a statement of:

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

Hint:

Remember the key mathematical forms of these laws: - Kick's law involves the logarithm of the size ratio. - Rittinger's law involves the difference in the reciprocals of the sizes (related to surface area). - Bond's law involves the difference in the reciprocals of the square roots of the sizes (related to crack propagation).

Answer 1

The Correct Option is B

Step 1: Understand the different laws governing crushing and grinding.
Several laws describe the energy requirements for size reduction of solid materials, such as crushing and grinding. The main ones are Kick's law, Rittinger's law, and Bond's law.
Step 2: Recall the statement of Kick's law.
Kick's law states that the work required for crushing a given weight of material to a fraction of its original size is the same for the same reduction ratio, regardless of the initial size. Mathematically, it can be expressed as: \[ W = K_K \log \left( \frac{D_i}{D_f} \right) \] where:
\( W \) is the work required per unit mass of material.
\( K_K \) is Kick's constant, which depends on the material.
\( D_i \) is the initial characteristic size (e.g., diameter).
\( D_f \) is the final characteristic size (e.g., diameter).
The statement in the question directly matches the mathematical formulation and description of Kick's law.
Step 3: Recall the statements of Rittinger's and Bond's laws for comparison.
Rittinger's law: States that the work required for crushing is proportional to the new surface area created. \[ W = K_R \left( \frac{1}{D_f} - \frac{1}{D_i} \right) \] where \( K_R \) is Rittinger's constant. Bond's law: States that the work required to form particles of size \( D_p \) from very large feed is proportional to the new crack length produced and is given by: \[ W = \frac{W_i}{\sqrt{D_{p,f}}} - \frac{W_i}{\sqrt{D_{p,i}}} \] where \( W_i \) is the work index, \( D_{p,i} \) is the 80\% passing size of the feed, and \( D_{p,f} \) is the 80\% passing size of the product. A simplified form often used relates energy to the square root of the size ratio.
Step 4: Consider Fick's law.
Fick's law describes diffusion and is not related to the energy requirements for crushing materials.
Step 5: Match the given statement with the correct law.
The statement "The work required for crushing a given material is proportional to the logarithm of the ratio between the initial and final diameters" is precisely the definition of Kick's law.
Step 6: Select the correct answer.
The statement is a statement of Kick's law.