Step 1: Understanding the Question:
The question asks to identify the scientific law that relates the energy needed for size reduction (crushing or grinding) to the increase in the surface area of the particles.
Step 2: Key Concepts and Theories:
In the field of mechanical operations, particularly comminution (size reduction), there are three main theories that estimate the energy requirement:
- Rittinger's Law: This law postulates that the energy consumed is directly proportional to the new surface area created. It is most applicable for fine grinding, where a large increase in surface area occurs.
- Kick's Law: This law states that the energy required is proportional to the logarithm of the reduction ratio. It is more accurate for coarse crushing of large particles.
- Bond's Law: This law provides a middle ground and states that the energy is proportional to the square root of the surface-to-volume ratio. It is useful for a wide range of particle sizes.
Step 3: Detailed Explanation:
- The question specifically asks for the law where energy is proportional to the "change in surface area."
- According to its definition, Rittinger's Law fits this description perfectly. The fundamental assumption is that all energy input is used to create new surfaces.
- Kick's Law relates energy to the size ratio, not the surface area.
- Bond's Law is an intermediate theory.
- Newton's Law relates to motion and force and is irrelevant to this context.
Step 4: Final Answer:
Therefore, Rittinger's Law is the correct answer as it directly links the energy for size reduction to the change in surface area.