Subtopic: Preservation of food by cooling and freezing
Question Statement:
1000 units of mixed fruit bar, each 100 g (surface area 0.01 m²), frozen from 70°C molten mass to -20°C frozen storage within 3 hours. c_p = 3.6 kJ/kg·K (before freezing, 70→0°C) and 1.97 kJ/kg·K (after freezing, 0→-20°C). Latent heat of crystallization = 250 kJ/kg. The cooling capacity required, in tons of refrigeration (TR), is:
Options:
(A) 0.77
(B) 1.43
(C) 1.66
(D) 4.32
Official Answer Key:
B
Step-by-Step Solution & Explanation
Total mass = 1000×0.1=100 kg. Sensible heat (70→0°C): 100×3.6×70=25,200 kJ. Latent heat: 100×250=25,000 kJ. Sensible heat (0→-20°C): 100×1.97×20=3,940 kJ. Total heat = 25,200+25,000+3,940=54,140 kJ over 3 h = 3×3600=10,800 s. Rate = 54,140/10,800=5.013 kW. 1 TR = 3.517 kW. Capacity = 5.013/3.517 = 1.425 ≈ 1.43 TR. Answer: B.
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