= 23.1 hp.
For a Carnot cycle, the efficiency is given by the equation, Carnot = 1 – TL/TH. We can rearrange this equation and substitute the given data of = 55% and TL = 60oF = 519,67 R to obtain the temperature of the heat source.
= 1156 R.
6 A homeowner is trying to decide between a high-efficiency natural gas furnace with an efficiency of 97% and a ground-source heat pump with a COP of 3.5. The unit costs of electricity and natural gas are $0.092/kWh and $1.42/therm (1 therm = 105 Btu = 105,505.6 kJ). Determine which system will have a lower energy cost.
The cost of each fuel can be compared for an equivalent amount of energy delivered to the house. With the furnace, 97% of the energy in the natural gas will be delivered to the house. Thus the cost to provide 1 kJ of heating with the gas furnace is
For the heat pump, the amount of heat delivered to the house is 3.5 times the electric power input. The cost to provide 1 kJ of heating with the heat pump is
Thus, the energy cost of the heat pump is lower. However, the heat pump will have a higher initial cost and the homeowner would have to do a financial analysis to see if the savings was worth the extra cost of the heat pump.
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