Subtopic: Concentration and drying of liquid foods – evaporators, tray, drum and spray dryers
Question Statement:
A single effect evaporator is used to concentrate orange fruit juice with a 2.7:1 concentration ratio of product solid to feed solid. The juice is fed to the evaporator at 100 kg·h⁻¹ and 30 °C, where the product moisture evaporates at 60 °C. The specific heat of juice is 3.9 kJ·kg⁻¹·°C⁻¹. The latent heat of vaporisation at 60 °C is 2450 kJ·kg⁻¹. Heat to accomplish the evaporation, in MJ·h⁻¹, is nearest to
Options:
(A) 165.96
(B) 117.06
(C) 154.26
(D) 142.56
Official Answer Key:
A
Step-by-Step Solution & Explanation
Step 1 — mass balance on solids. Solids are conserved. A concentration ratio of 2.7:1 (product solid fraction : feed solid fraction) means the product stream is 1/2.7 of the feed mass:
Product = 100/2.7 = 37.04 kg·h⁻¹
Water evaporated = 100 − 37.04 = 62.96 kg·h⁻¹
Step 2 — sensible heat to raise the whole feed from 30 °C to the boiling temperature 60 °C:
Q_sensible = m c ΔT = 100 × 3.9 × (60 − 30) = 11,700 kJ·h⁻¹
Step 3 — latent heat to vaporise the water at 60 °C:
Q_latent = 62.96 × 2450 = 154,252 kJ·h⁻¹
Step 4 — total heat:
Q = 11,700 + 154,252 = 165,952 kJ·h⁻¹ = 165.96 MJ·h⁻¹
(Option (C) 154.26 is the latent-heat-only trap — it omits the sensible heating.)
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