Numerical Solution: Kick’s Law

 

Numerical Solution: Kick’s Law (Size Reduction)

Calculate the energy required to reduce particle size from 50 mm to 12.5 mm using Kick’s law, given Kk = 3.2 kJ/kg.

Given

• Initial particle size, $D_1 = 50$mm

• Final particle size, $D_2 = 12.5$ mm

• Kick’s constant, $K_k = 3.2$ kJ/kg

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Kick’s Law

$$E = K_k \ln\!\left(\frac{D_1}{D_2}\right)$$

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Step-wise Calculation

$$\frac{D_1}{D_2} = \frac{50}{12.5} = 4$$
$$E = 3.2 \times \ln(4)$$
$$\ln(4) = 1.386$$
$$E = 3.2 \times 1.386 = 4.435 \text{ kJ/kg}$$

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Final Answer

$$\boxed{E \approx 4.44 \text{ kJ/kg}}$$

Energy required to reduce the particle size from 50 mm to 12.5 mm is approximately 4.44 kJ/kg.