Subtopic: Mechanics and energy requirement in size reduction of agriculture produce
Question Statement:
Which of the following classical size reduction energy laws and their underlying hypotheses are CORRECTLY stated?
Options:
(A) Rittinger's law states that energy required for size reduction is directly proportional to the new surface area created: $E = C_R \left(\frac{1}{d_2} - \frac{1}{d_1}\right)$
(B) Kick's law states that energy required is proportional to the reduction ratio of the volume: $E = C_K \ln\left(\frac{d_1}{d_2}\right)$
(C) Bond's law states that energy is proportional to the crack length formed: $E = W_i \left(\frac{1}{\sqrt{d_2}} - \frac{1}{\sqrt{d_1}}\right)$
(D) Rittinger's law is most applicable to coarse crushing operations while Kick's law applies to ultra-fine grinding
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
1. Rittinger's law assumes surface energy dominance: $dE = -C \frac{dx}{x^2} \implies E = C_R (\frac{1}{d_2} - \frac{1}{d_1})$. (Statement A True)
2. Kick's law assumes elastic stress volume deformation: $dE = -C \frac{dx}{x} \implies E = C_K \ln(d_1 / d_2)$. (Statement B True)
3. Bond's law bridges intermediate grinding: $dE = -C \frac{dx}{x^{1.5}} \implies E = 10 W_i (\frac{1}{\sqrt{d_2}} - \frac{1}{\sqrt{d_1}})$. (Statement C True)
4. The domain of validity is inverted in Statement D: Kick's law applies to coarse crushing ($d > 50\text{ mm}$), Bond applies to intermediate grinding, and Rittinger applies to ultra-fine grinding ($d < 0.05\text{ mm}$) where new surface area creation dominates. (Statement D False)