A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is 280 K. Heat loss from the auditorium is 15 kW. The power consumption of the heat pump is _________ kW (rounded off to 2 decimal places).
A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is 280 K. Heat loss from the auditorium is 15 kW. The power consumption of the heat pump is _________ kW (rounded off to 2 decimal places).
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Solution and Explanation
Given: \[ T_H = 300 \ {K}, \quad T_L = 280 \ {K}, \quad Q_H = 15 \ {kW} \] For a reversed Carnot cycle, the Coefficient of Performance (COP) of the heat pump is: \[ {COP}_{{HP}} = \frac{T_H}{T_H - T_L} = \frac{300}{300 - 280} = \frac{300}{20} = 15 \] Power consumption of the heat pump is given by: \[ {COP}_{{HP}} = \frac{Q_H}{W} \Rightarrow W = \frac{Q_H}{{COP}_{{HP}}} = \frac{15}{15} = 1.00 \ {kW} \]
Correct Answer: 1.00 kW
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