Subtopic: Mechanics and energy requirement in size reduction of agriculture produce
Question Statement:
According to Rittinger's law of comminution, the energy required to grind a material from an average feed diameter $L_1 = 10\text{ mm}$ to product diameter $L_2 = 2\text{ mm}$ is $12\text{ kJ/kg}$. The energy required in $\text{kJ/kg}$ to grind the same material from feed diameter $10\text{ mm}$ to product diameter $1\text{ mm}$ is ________ (round off to 1 decimal place).
Answer Key:
27.0
Step-by-Step Solution & Explanation
Rittinger's law states that energy $E$ is proportional to new surface area created:
$E = K_R \left( \frac{1}{L_2} - \frac{1}{L_1} \right)$
For the first reduction ($L_1 = 10\text{ mm}$, $L_2 = 2\text{ mm}$):
$12 = K_R \left( \frac{1}{2} - \frac{1}{10} \right) = K_R (0.5 - 0.1) = 0.4 K_R \implies K_R = \frac{12}{0.4} = 30$
For the second reduction ($L_1 = 10\text{ mm}$, $L_2' = 1\text{ mm}$):
$E' = 30 \left( \frac{1}{1} - \frac{1}{10} \right) = 30 (1 - 0.1) = 30 \times 0.9 = 27.0\text{ kJ/kg}$