Question Bank • QB_DFE_038 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Preservation of Food

Subtopic: Refrigeration and cold storage basics and applications

Question Statement:

A cold storage room holds $10000\text{ kg}$ ($10\text{ tonnes}$) of fresh apples. The apples are pulled down from $25^\circ\text{C}$ to $5^\circ\text{C}$ over a period of $24\text{ hours}$ ($86400\text{ s}$). The specific heat of apples is $3.60\text{ kJ/(kg}\cdot\text{K)}$. In addition, the average respiration heat generation rate of the apples during this cooling period is $0.04\text{ W/kg}$. The total product cooling heat load in $\text{kW}$ is ________ (round off to 2 decimal places).

Answer Key:

8.73

Step-by-Step Solution & Explanation

1. Sensible heat to be extracted: $Q_s = m \cdot c_p \cdot \Delta T = 10000\text{ kg} \times 3.60\text{ kJ/(kg}\cdot\text{K)} \times (25 - 5)^\circ\text{C} = 720000\text{ kJ}$ 2. Average sensible cooling rate: $\dot{Q}_s = \frac{720000\text{ kJ}}{86400\text{ s}} = 8.3333\text{ kW}$ 3. Respiration heat generation rate: $\dot{Q}_{resp} = 10000\text{ kg} \times 0.04\text{ W/kg} = 400\text{ W} = 0.4000\text{ kW}$ 4. Total product heat load: $\dot{Q}_{total} = \dot{Q}_s + \dot{Q}_{resp} = 8.3333 + 0.4000 = 8.7333\text{ kW} \approx 8.73\text{ kW}$
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