121 A home is heated with an airtoair heat pump The manufact

12.1 A home is heated with an air-to-air heat pump. The manufacturer reports a COP of 3.1 forthe heat pump. If the home is losing 25,600 Btu/hr, and electricity costs $0.085 per kWhr, what is the daily cost of heating this home?

12.2 Assume the homeowner from problem 12.1 investigates upgrading the home heating system to geothermal with a COP of 4.3. What is the new hourly cost of operation?

12.3 Assuming the heat season is five months with an average heat loss of 18,500 Btu/hr. If thecapital cost of the geothermal system is $17,300, what is the payback period for upgradingto geothermal from a heat pump? Use the COP values in problems 12.1 and 12.2.

Solution

25,600 Btu/hr = 27,009 KJ/hr

COP = 3.1 Q1= 27,009 KJ/hr

Therefor, COP=Q1/W

Hence,

W= Q1/COP = 27,009 /(3.1*3600) = 2.42 kWhr

Now, electricity costs $0.085 per kWhr. So, 2.42*0.085 = $0.2057*24= $4.93 per day

Now for COP = 4.3 it will be,

W= Q1/COP = 27,009 /(4.3*3600) = 1.74 kWhr

ow, electricity costs $0.085 per kWhr. So, 1.74*0.085 = $0.1483

For COP of 3.1,

18500 Btu/hr = 19518.533 kJ/hr

W= Q1/COP = 19,518 /(3.1*3600) = 1.74 kWhr*$0.085*24*30*5 = $ 535.17

So it will be like 17,300/535.17 = 32 heat seasons or 161 months

For COP of 4.3,

18500 Btu/hr = 19518.533 kJ/hr

W= Q1/COP = 19,518 /(4.3*3600) = 1.74 kWhr*$0.085*24*30*5 = $ 385.82

So it will be like 17,300/385.82 = 44.83 heat seasons or 224 months