Subtopic: Preservation of food by cooling and freezing
Question Statement:
An industrial dairy heat pump utilizes waste heat from milk chilling at $T_L = 15.0^\circ\text{C} = 288.15\text{ K}$ to supply hot water for sanitary cleaning at $T_H = 75.0^\circ\text{C} = 348.15\text{ K}$. The theoretical maximum Carnot Coefficient of Performance of this heat pump ($\text{COP}_{\text{HP}} = \frac{T_H}{T_H - T_L}$) is ________ (round off to two decimal places).
Answer Key:
5.80
Step-by-Step Solution & Explanation
The theoretical maximum Carnot COP for a heat pump is:
$\text{COP}_{\text{HP}} = \frac{T_H}{T_H - T_L} = \frac{348.15\text{ K}}{348.15\text{ K} - 288.15\text{ K}} = \frac{348.15}{60.0} = 5.8025 \approx 5.80$
(Note: $\text{COP}_{\text{HP}} = \text{COP}_{\text{Ref}} + 1 = 4.80 + 1 = 5.80$).