Question:
Which of the following laws are based on stress analysis of plastic deformation within the elastic limit?
Which of the following laws are based on stress analysis of plastic deformation within the elastic limit?
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To remember the applicability of size reduction laws:
- Kick's Law \(\rightarrow\) Coarse crushing (based on bulk volume/plastic deformation within elastic limits).
- Bond's Law \(\rightarrow\) Intermediate grinding (based on crack propagation).
- Rittinger's Law \(\rightarrow\) Fine grinding (based on new surface area created).
- Kick's Law \(\rightarrow\) Coarse crushing (based on bulk volume/plastic deformation within elastic limits).
- Bond's Law \(\rightarrow\) Intermediate grinding (based on crack propagation).
- Rittinger's Law \(\rightarrow\) Fine grinding (based on new surface area created).
Updated On: Jul 23, 2026
- Kick's law
- Rittinger's law
- Bond's law
- Planks's law
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Size reduction (milling, grinding, or crushing) is a common unit operation in dairy and food processing.
Reducing the size of solid materials requires energy to overcome molecular cohesive forces and create new surfaces.
Three classical mathematical models predict the energy required for size reduction: Rittinger's law, Kick's law, and Bond's law.
Step 2: Detailed Explanation:
Let us analyze the physiological basis of Kick's law:
- Kick's Law:
Kick's law assumes that the energy required for a given size reduction is directly proportional to the ratio of the initial and final dimensions of the material.
It is expressed as:
\[ E = K_K \ln\left(\frac{D_1}{D_2}\right) \]
where \(D_1\) is the initial size, \(D_2\) is the final size, and \(K_K\) is Kick's constant.
This model is based on the stress analysis of plastic deformation within the elastic limit of the material.
It assumes that the energy required to deform a unit volume of material is constant, regardless of its original size.
Consequently, it is highly accurate for coarse crushing operations, where most energy is used to deform the bulk material before fracture occurs.
- Rittinger's Law:
Based on the hypothesis that the energy required is proportional to the new surface area created during grinding.
It is highly accurate for fine grinding operations, where new surface area creation dominates energy consumption.
- Bond's Law:
An intermediate model assuming that the energy required is proportional to the length of the cracks formed during fracture.
Step 3: Final Answer:
Kick's law is based on the stress analysis of plastic deformation within the elastic limit.
Size reduction (milling, grinding, or crushing) is a common unit operation in dairy and food processing.
Reducing the size of solid materials requires energy to overcome molecular cohesive forces and create new surfaces.
Three classical mathematical models predict the energy required for size reduction: Rittinger's law, Kick's law, and Bond's law.
Step 2: Detailed Explanation:
Let us analyze the physiological basis of Kick's law:
- Kick's Law:
Kick's law assumes that the energy required for a given size reduction is directly proportional to the ratio of the initial and final dimensions of the material.
It is expressed as:
\[ E = K_K \ln\left(\frac{D_1}{D_2}\right) \]
where \(D_1\) is the initial size, \(D_2\) is the final size, and \(K_K\) is Kick's constant.
This model is based on the stress analysis of plastic deformation within the elastic limit of the material.
It assumes that the energy required to deform a unit volume of material is constant, regardless of its original size.
Consequently, it is highly accurate for coarse crushing operations, where most energy is used to deform the bulk material before fracture occurs.
- Rittinger's Law:
Based on the hypothesis that the energy required is proportional to the new surface area created during grinding.
It is highly accurate for fine grinding operations, where new surface area creation dominates energy consumption.
- Bond's Law:
An intermediate model assuming that the energy required is proportional to the length of the cracks formed during fracture.
Step 3: Final Answer:
Kick's law is based on the stress analysis of plastic deformation within the elastic limit.
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