Subtopic: Mechanics and energy requirement in size reduction of agriculture produce
Question Statement:
Using Kick's law $E = K_K \ln\left(\frac{d_1}{d_2}\right)$, crushing a material from $10.0\text{ mm}$ to $5.0\text{ mm}$ consumes $5.0\text{ kWh/tonne}$. The energy required to crush the same material from $5.0\text{ mm}$ to $2.5\text{ mm}$ in $\text{kWh/tonne}$ is ________ (answer in integer).
Answer Key:
5
Step-by-Step Solution & Explanation
According to Kick's law, the energy consumed is proportional to the reduction ratio ($d_1 / d_2$):
• Initial reduction ratio $R_1 = \frac{10.0}{5.0} = 2.0$, requiring $E_1 = K_K \ln(2.0) = 5.0\text{ kWh/tonne}$.
• Second reduction ratio $R_2 = \frac{5.0}{2.5} = 2.0$.
Since both reduction ratios are identical ($R_1 = R_2 = 2.0$), the energy required is identical: $E_2 = 5.0\text{ kWh/tonne}$.