With an actual coefficient of performance, gamma = 4.0, a heat pump is used to p

Question

With an actual coefficient of performance, gamma = 4.0, a heat pump is used to provide the heat at an average time rate of 120 kWh/day (1 kWh=3, 6000 kJ) to maintain a building at 290 K on a day, when the outside temperature is 261 K. The cost of electricity is $0.10/kWh, please: Calculate the actual daily electricity used by the heat pump, W_cyce, in kWh/day; Calculate the cost of actual daily electricity used, cycle, in $ day; Evaluate the theoretical maximum coefficient of performance, gamma_max Calculate the theoretical minimum daily electricity required by the heat pump, W_min, in kWh/day; and its cost, $min, in s/day; If an electrical resistor heater is instead used to provide the same time rate of heat of 120 kWh/day, please calculate its cost, $resistor, in $/day; Compare the cost using heat pump with the cost using electrical resistor heater.

Explanation / Answer

(a) CP = QH/W

=> 4 = 120/W

=> W = 30 kWh/day

(b) Cost = 0.1*W

=> cost = 3 dollars/day

(c) CPtheoretical = TH/(TH - TC)

=> CPtheoretical = 290/(290-261)

=> CPtheoretical = 10

(d) CPtheoretical = QH/Wmin

=> Wmin = 120/10

=> Wmin = 12 kWh/day

(e) Cost = 0.1*120

=> Cost = 12 dollars/day

(f) Costheat pump = 3 dollars/day

Costelectrical-resistor heater = 12 dollara/day = 300% greater than Costheat pump

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