Subtopic: Mechanics and energy requirement in size reduction of agriculture produce
Question Statement:
A pulse mill grinds Bengal gram of 2 mm volume-surface mean diameter to powder of 100 μm volume-surface mean diameter. The ratio of Rittinger's to Kick's constant in the grinding operation is
Options:
(A) 0.317 kWh kg⁻¹
(B) 3.15 mm
(C) 315.34 μm
(D) 152.793 kWh ton⁻¹
Official Answer Key:
C
Step-by-Step Solution & Explanation
Rittinger's law: E = K_R(1/D₂ − 1/D₁). Kick's law: E = K_K·ln(D₁/D₂). Equating the same specific energy E: K_R/K_K = ln(D₁/D₂) / (1/D₂ − 1/D₁). With D₁=2 mm=2000 μm, D₂=100 μm: ln(2000/100)=ln(20)=2.996; (1/100−1/2000)=0.0095 μm⁻¹. Ratio = 2.996/0.0095 = ≈315.34 μm (the ratio carries units of length, since Rittinger's constant has units of energy·length and Kick's has units of energy).
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