Question

Crushing efficiency is the ratio of

• A. Surface energy created by the crushing to the energy absorbed by the solid
• B. The energy absorbed by the solid to that fed to the machine
• C. The energy fed to the machine to the surface energy created by the crushing
• D. The energy absorbed by the solid to the surface energy created by the crushing

Hint:

Size Reduction Energy Laws: - Crushing Efficiency = \(\frac{\text{Surface Energy Created}}{\text{Energy Absorbed by Solid}}\). - Rittinger's Law states that energy required is directly proportional to the new surface area created. - Kick's Law states that energy required is proportional to the volume reduction ratio.

Answer 1

The Correct Option is A

Concept: During any industrial size reduction operation (such as crushing or grinding), a significant amount of mechanical energy supplied to the equipment is lost. Much of it is dissipated as heat, sound, vibration, and mechanical friction within the moving parts of the machine. Only a very small fraction of the total energy input is actually utilized to break the chemical bonds of the solid and create new surface areas. According to Rittinger's law and basic surface thermodynamics, the true theoretical work required for size reduction is directly proportional to the new surface area generated. Therefore, the mechanical or crushing efficiency (\(\eta_c\)) is defined fundamentally as the ratio of the theoretical energy needed to create the new surface area to the actual energy absorbed or consumed by the material during the fracture process.

Step 1: Defining the mathematical formulation for crushing efficiency.
Mathematically, we can express this relationship clearly as follows: \[ \text{Crushing Efficiency } (\eta_c) = \frac{\text{Surface Energy Created by Crushing}}{\text{Total Mechanical Energy Absorbed by the Solid}} \] Where:

• Surface Energy Created = \(\Delta A \cdot \gamma_s\) (where \(\Delta A\) is the increase in surface area and \(\gamma_s\) is the specific surface energy per unit area).

• Energy Absorbed = The portion of the input energy that enters the material structure to cause strain, deformation, and eventual cracking.

Step 2: Analyzing the physical significance of the ratio parameters.
In real-world crushing equipment, this efficiency is typically very low, often ranging between \(0.5\%\) and \(2\%\). This means that over \(98\%\) of the energy absorbed by the solid is converted into internal thermal energy (heat) and plastic deformation rather than forming new surfaces.

Step 3: Matching the definition with the provided options.
Reviewing the options, Option (A) correctly identifies this efficiency as the ratio of the newly created surface energy to the total energy absorbed by the solid during the size reduction process.