Which size reduction law states that the work used to reduce the particle size is proportional to the square root of diameter of particle produced?

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Prepare for the Manor Preboards Module 5 Test with multiple choice questions and detailed explanations. Enhance your study with structured modules to master the test content efficiently.

Multiple Choice

Which size reduction law states that the work used to reduce the particle size is proportional to the square root of diameter of particle produced?

Explanation:
When we look at how much energy is needed to grind particles, different empirical laws tie the work to how big the particles are after grinding. Bond's law expresses the work required to reduce a particle from an initial diameter D0 to a final diameter Df as proportional to the difference of the square roots: W ∝ √D0 − √Df (often written W = K(√D0 − √Df)). This square-root relationship is the hallmark of Bond’s approach, sitting between the extremes of other laws that emphasize simple size ratios or surface area change. So when a statement says the work to reduce particle size is proportional to the square root of the diameter of the produced particle, it’s describing Bond’s law. It captures the idea that energy scales with particle size in a way that isn’t purely linear or solely based on surface area, making it a good fit for many intermediate grinding conditions.

When we look at how much energy is needed to grind particles, different empirical laws tie the work to how big the particles are after grinding. Bond's law expresses the work required to reduce a particle from an initial diameter D0 to a final diameter Df as proportional to the difference of the square roots: W ∝ √D0 − √Df (often written W = K(√D0 − √Df)). This square-root relationship is the hallmark of Bond’s approach, sitting between the extremes of other laws that emphasize simple size ratios or surface area change.

So when a statement says the work to reduce particle size is proportional to the square root of the diameter of the produced particle, it’s describing Bond’s law. It captures the idea that energy scales with particle size in a way that isn’t purely linear or solely based on surface area, making it a good fit for many intermediate grinding conditions.

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