Subtopic: Preservation of food by cooling and freezing
Question Statement:
Freshly harvested shrimps of 100 kg having initial temperature of 25 °C are frozen to −18 °C. The specific heat (c_p) of shrimp above and below freezing point (0 °C) are 3.64 kJ·kg⁻¹·°C⁻¹ and 2.01 kJ·kg⁻¹·°C⁻¹, respectively. Considering the latent heat of fusion as 240 kJ·kg⁻¹, the heat load removed during the process, in kJ, is __________. (Rounded off to 1 decimal place)
Official Answer Key:
36710.0 to 36730.0
Step-by-Step Solution & Explanation
The total heat load has three distinct components, because the product passes through a phase change.
Step 1 — sensible heat above freezing (25 °C → 0 °C), using c_p above freezing:
Q₁ = m c_p ΔT = 100 × 3.64 × (25 − 0) = 9100 kJ
Step 2 — latent heat of fusion (freezing at 0 °C):
Q₂ = m L = 100 × 240 = 24,000 kJ
Step 3 — sensible heat below freezing (0 °C → −18 °C), using c_p below freezing:
Q₃ = m c_p ΔT = 100 × 2.01 × 18 = 3618 kJ
Step 4 — total heat removed:
Q = 9100 + 24,000 + 3618 = 36,718.0 kJ
(Note that the latent heat term alone accounts for about 65 % of the load — which is why freezing is so much more energy-intensive than simple chilling.)
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