Question Bank • QB_DFE_PF_008 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Preservation of Food

Subtopic: Preservation of food by cooling and freezing

Question Statement:

A domestic refrigeration plant operates on an ideal vapor-compression refrigeration cycle using R134a. The evaporator absorbs heat at $T_L = -10.0^\circ\text{C} = 263.15\text{ K}$ and the condenser rejects heat at $T_H = 40.0^\circ\text{C} = 313.15\text{ K}$. The Carnot theoretical maximum Coefficient of Performance of this refrigeration system ($\text{COP}_{\text{Carnot}} = \frac{T_L}{T_H - T_L}$) is ________ (round off to two decimal places).

Answer Key:

5.26

Step-by-Step Solution & Explanation

Multi-Approach Solution: **Method 1: Carnot COP Definition** $\text{COP}_{\text{Carnot}} = \frac{T_L}{T_H - T_L}$ Given absolute temperatures: $T_L = 273.15 - 10.0 = 263.15\text{ K}$ $T_H = 273.15 + 40.0 = 313.15\text{ K}$ $T_H - T_L = 313.15 - 263.15 = 50.0\text{ K}$ $\text{COP} = \frac{263.15}{50.0} = 5.263 \approx 5.26$ **Method 2: Heat/Work Ratio** $q_L = T_L \Delta s, \quad w = (T_H - T_L) \Delta s \implies \text{COP} = \frac{q_L}{w} = \frac{263.15}{50.0} = 5.26$
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