Discussion
Applying Kick's law with a constant of \( 8 \) kWh per tonne, reducing from \( 20 \) mm to \( 5 \) mm requires
Answer: A
Correct answer: 11.1 kWh per tonne
Kick's law makes the energy depend on the ratio of sizes rather than on their absolute values:
\[ E = K_K \ln \frac{x_1}{x_2} = 8 \ln \frac{20}{5} = 8 \ln 4 = 8 \times 1.386 = 11.1\ \mathrm{kWh/tonne} \]
Because only the ratio enters, Kick's law predicts the same energy for 20 mm to 5 mm as for 4 mm to 1 mm - which is why it describes coarse crushing well and fine grinding badly, where Rittinger's surface-based law fits better.
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