Step 1: Understanding the Problem:
This question asks for the fundamental assumption regarding energy consumption in solid size-reduction as stated by Rittinger's Law.
Step 2: Key Formula or Approach:
Rittinger's Law is one of three classical hypotheses used to estimate energy requirements in milling and size reduction.
The mathematical expression is:
\[ E = K_R \left( \frac{1}{d_2} - \frac{1}{d_1} \right) \]
where $E$ is the energy input per unit mass, $K_R$ is Rittinger's constant, $d_1$ is the feed particle size, and $d_2$ is the product particle size.
Step 3: Detailed Explanation:
• Rittinger's hypothesis assumes that size reduction is a surface-dominated process. The energy required to break a solid particle is spent on creating new surfaces by overcoming cohesive forces.
• Therefore, the mechanical work or energy input is directly proportional to the change in surface area of the material.
• Kick's Law assumes that the energy consumed is proportional to the ratio of reduction or the volume/mass of the material, which works better for coarse crushing.
• Bond's Law assumes that the energy required is proportional to the length of the cracks formed, which is intermediate between Rittinger's and Kick's models.
Step 4: Final Answer:
Hence, Rittinger's Law assumes that energy consumed is proportional to the new surface area created.