GATE AG 2008 • Q72 MCQ • 2 Marks

Section 6: Agricultural Process Engineering

Size Reduction and Material Handling

Subtopic: Mechanics and energy requirement in size reduction of agriculture produce

Question Statement:

A material consisting of 20 mm particles is crushed to an average size of 5 mm and requires 18 kJ kg⁻¹ energy for this size reduction. If other conditions are similar, the energy required (kJ kg⁻¹) to crush the material from 25 mm to 3 mm needs to be calculated. The energy requirement calculated using Kick's law will be

Options:

  • (A) 72.39
  • (B) 52.76
  • (C) 27.55
  • (D) 14.85

Official Answer Key:

C

Step-by-Step Solution & Explanation

Kick's law: E = K_K·ln(L₁/L₂). Calibrate: 18 = K_K·ln(20/5) = K_K·ln4 = K_K×1.3863 → K_K = 12.98. Apply to 25→3 mm: E = 12.98×ln(25/3) = 12.98×2.1203 = 27.53 ≈ 27.55 kJ/kg.

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