help A Carnot heat pump is to be used for heating house in winter. The house tem

Question

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A Carnot heat pump is to be used for heating house in winter. The house temperature is set at 25degreeC. One day the outdoor temperature is 2degreeC. The house is estimated to lose heat at a rate 55000kJ/h (which equal to Qout of the heat pump). Determine the total electrical work the heat pump can consume on that day; 2) If the heat pump consumes 6.6kW of power while operating, how long the heat pump ran on that day? 3) If the average price for electricity is 8.5 cent per kWh, what is the total cost?

Explanation / Answer

Here

T1= 2+273=275 K ,             T2=25+273=298 K

Qout= 55000kJ/h=55000/3600 kJ/s=15.277 kJ/s

For carnot heat pump COP= T2/(T2-T1)=298/(298-275)=12.956

work cosumption rate = Qout/COP=15.277/12.956=1.18 kW

(a) total electric work consumption fo a day(12h)= 1.18*12 kWh=14.16 kWh

(b) total time for which heat pump operated with 6.6 kW rate= 14.16/6.6= 2.145 h

(c) Total cost of electricity=14.16*8.5=120.36 cents

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