Subtopic: Mechanics and energy requirement in size reduction of agriculture produce
Question Statement:
Which of the following statements regarding size reduction comminution laws for agricultural produce are CORRECT?
Options:
(A) Rittinger's law states that the energy consumed is directly proportional to the new surface area created ($E \propto \Delta A$)
(B) Kick's law assumes that energy required is directly proportional to the reduction ratio $\ln(L_1 / L_2)$
(C) Bond's law states that energy required is inversely proportional to the square root of product size ($E \propto 1/\sqrt{L_2} - 1/\sqrt{L_1}$)
(D) Kick's law applies best to fine grinding, while Rittinger's law applies best to coarse crushing
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
1. Rittinger's law ($n=2$ in Walker's general differential comminution equation $dE/dL = -C/L^n$) assumes energy is proportional to newly generated surface area. (Statement A is True)
2. Kick's law ($n=1$) assumes energy is proportional to the logarithm of the ratio of initial to final sizes $\ln(L_1/L_2)$. (Statement B is True)
3. Bond's law ($n=1.5$) states energy is proportional to crack length, leading to $E = 10 W_i \left(\frac{1}{\sqrt{L_2}} - \frac{1}{\sqrt{L_1}}\right)$. (Statement C is True)
4. Kick's law applies best to COARSE crushing (elastic deformation range), whereas Rittinger's law applies best to FINE grinding (where surface forces dominate). Thus Statement D is inverted and False.