When making large purchases like an air conditioning unit, the difference in price between units can...

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When making large purchases like an air conditioning unit, the difference in price between units can often deter consumers from selecting higher end, more expensive units. However, the conscious consumer should recognize that the question is not which unit is cheaper up front, but instead which unit will cost the least over the lifetime of the unit. Consider a dwelling that does not require air conditioning 25% of the year (365 days). When the dwelling does require AC, it receives heat from the surrounding environment at an average rate of Qenv = 20 kW. There are also people and appliances in the home that generate energy at an average rate of Qgen = 1 kW. a) Create a schematic of the dwelling and the air conditioning unit. Clearly identify any energy interactions between the dwelling and the surroundings, the dwelling and the AC unit, and the AC unit and the surroundings. b) If the initial cost of a particular AC unit is A and the cost of electricity is B, in cost-per-kilowatt- hour (kWh), develop an equation for the cost (C) to condition the air in the dwelling as a function of time (t), in years. To do this, you must build the conversion between years and hours into your equation. Your equation should depend only an A, B, t, COPR, and Qload, where COPR is the coefficient of performance of the AC unit and Q load is the average cooling load of the AC unit when it is operating. c) The purchase and installation cost and COPR of two different AC units is given below. If the cost of electricity is 16 cents per kWh, how many years would it take for unit 2 to "make up" for the fact that its purchase and installation cost is greater than that of unit 1? If the average lifespan of an AC unit is around 15 years, which unit is the better financial investment? Purchase and Installation Cost CQPR Unit 1 Unit 2 $5000 $7500 2.5 2.7 d) How would changing the cost of electricity alter your answer to part c? When making large purchases like an air conditioning unit, the difference in price between units can often deter consumers from selecting higher end, more expensive units. However, the conscious consumer should recognize that the question is not which unit is cheaper up front, but instead which unit will cost the least over the lifetime of the unit. Consider a dwelling that does not require air conditioning 25% of the year (365 days). When the dwelling does require AC, it receives heat from the surrounding environment at an average rate of Qenv = 20 kW. There are also people and appliances in the home that generate energy at an average rate of Qgen = 1 kW. a) Create a schematic of the dwelling and the air conditioning unit. Clearly identify any energy interactions between the dwelling and the surroundings, the dwelling and the AC unit, and the AC unit and the surroundings. b) If the initial cost of a particular AC unit is A and the cost of electricity is B, in cost-per-kilowatt- hour (kWh), develop an equation for the cost (C) to condition the air in the dwelling as a function of time (t), in years. To do this, you must build the conversion between years and hours into your equation. Your equation should depend only an A, B, t, COPR, and Qload, where COPR is the coefficient of performance of the AC unit and Q load is the average cooling load of the AC unit when it is operating. c) The purchase and installation cost and COPR of two different AC units is given below. If the cost of electricity is 16 cents per kWh, how many years would it take for unit 2 to "make up" for the fact that its purchase and installation cost is greater than that of unit 1? If the average lifespan of an AC unit is around 15 years, which unit is the better financial investment? Purchase and Installation Cost CQPR Unit 1 Unit 2 $5000 $7500 2.5 2.7 d) How would changing the cost of electricity alter your answer to part c?