Subtopic: Mechanics and energy requirement in size reduction of agriculture produce
Question Statement:
Energy required to grind a given mass of particles from a mean diameter of 12 mm to 4 mm is 12 kJ kg⁻ ¹. If energy consumed to grind the same mass of particles of 2 mm mean diameter to x mm mean diameter is 252 kJ kg⁻¹, the value of x using Rittinger’s Law will be _______.
Official Answer Key:
0.249 to 0.251
Step-by-Step Solution & Explanation
Rittinger's Law: E = K_R·[(1/d₂) − (1/d₁)], where d₁ = initial size, d₂ = final size.
Find K_R: 12 = K_R·[(1/4) − (1/12)] = K_R·[(3−1)/12] = K_R·(2/12) = K_R/6 ⇒ K_R = 72 (kJ·mm/kg).
Apply to second grind (2 mm → x mm): 252 = 72·[(1/x) − (1/2)]
252/72 = 3.5 = 1/x − 0.5 ⇒ 1/x = 4.0 ⇒ x = 0.25 mm, matching the accepted range exactly.
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