Question

The crushing efficiency of a crusher is the ratio of

• A. energy absorbed by the solid to energy supplied to the crusher
• B. energy supplied to the crusher to surface energy created by crushing
• C. surface energy created by crushing to energy absorbed by the solid
• D. surface energy created by crushing to energy supplied to the crusher

Hint:

Distinguish between the "overall efficiency" of a process (useful output / total input) and more specific efficiencies. "Crushing efficiency" focuses on the material's fracture process itself, separating it from the mechanical losses of the machine.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Efficiency, in general, is a measure of how effectively an input is converted into a useful output. In the context of crushing or comminution, the goal is to break down solid particles, which involves creating new surface area. The energy required to create this new surface is the "useful" energy output. The energy actually put into the solid material to cause fracture is the "input" energy for the material itself.

Step 2: Detailed Explanation:
Let's define the terms involved: -

Energy supplied to the crusher (\(E_{supplied}\)): This is the total electrical or mechanical energy fed into the crushing machine. Much of this is lost as heat, sound, and friction in the machine's moving parts. -

Energy absorbed by the solid (\(E_{absorbed}\)): This is the fraction of the supplied energy that is actually transferred to the solid particles to cause deformation and fracture. The rest of \(E_{supplied}\) is lost. -

Surface energy created by crushing (\(E_{surface}\)): This is the theoretical minimum energy required to create the new surfaces during fracture. It's the useful work done on the material. There are different definitions of efficiency in crushing, but the most fundamental one, often called the "crushing efficiency," relates the theoretical minimum energy required to the energy actually used by the material. - Overall Efficiency: \( \frac{\text{Surface energy created}}{\text{Energy supplied to the crusher}} \). This value is very low, typically less than 1%. - Crushing Efficiency: This measures how effectively the energy absorbed by the solid is used to create new surfaces. \[ \text{Crushing Efficiency} = \frac{\text{Useful Energy Output}}{\text{Energy Input to Material}} = \frac{\text{Surface energy created by crushing}}{\text{Energy absorbed by the solid}} \] This definition isolates the efficiency of the material's fracture process from the mechanical inefficiencies of the crusher machine. Let's evaluate the options based on this understanding: - (A) This is a measure of the crusher's mechanical efficiency (how well it transfers energy to the solid). - (B) This is the inverse of the overall efficiency, which is incorrect. - (C) This correctly defines the ratio of the ideal work of creating new surface area to the actual energy absorbed by the material to achieve this. - (D) This is the overall efficiency of the crusher system, which is different from the specific "crushing efficiency." The question asks for "crushing efficiency," which is best defined by option (C) as it focuses on the material's response rather than the machine's.

Step 3: Final Answer:
The crushing efficiency is the ratio of the surface energy created by crushing to the energy absorbed by the solid. This corresponds to option (C).