Question

Consider a building whose annual air-conditioning load is estimated to be \(40,000 \mathrm{kWh}\) in an area where the unit cost of electricity is \(\$ 0.10 / \mathrm{kWh}\). Two air conditioners are considered for the building. Air conditioner A has a seasonal average COP of 2.3 and costs \(\$ 5500\) to purchase and install. Air conditioner B has a seasonal average COP of 3.6 and costs \(\$ 7000\) to purchase and install. All else being equal, determine which air conditioner is a better buy.

Short answer

Answer: Air Conditioner A is a better buy considering the first-year cost.

Step-by-step solution

Calculate Annual Running Cost for Each Air Conditioner

To calculate the annual running cost, we'll need to find the energy consumption for each air conditioner and multiply it by the cost of electricity per kWh. For Air Conditioner A: Energy Consumption = Annual Load (kWh) / COP_A Annual Running Cost_A = Energy Consumption_A * Electricity Cost per kWh For Air Conditioner B: Energy Consumption = Annual Load (kWh) / COP_B Annual Running Cost_B = Energy Consumption_B * Electricity Cost per kWh

Calculate Total Cost of Each Air Conditioner Over a Year

To calculate the total cost of each air conditioner over a year, we need to add the initial purchase and installation cost to the annual running cost. Total Cost_A = Purchase and Installation Cost_A + Annual Running Cost_A Total Cost_B = Purchase and Installation Cost_B + Annual Running Cost_B

Comparing the Total Costs

After calculating the total costs for both air conditioners, we can compare them to determine which is a better buy. If Total Cost_A < Total Cost_B, then Air Conditioner A is a better buy. If Total Cost_B < Total Cost_A, then Air Conditioner B is a better buy. Now, let's apply these steps to the given problem:

Values and Calculation

Annual Load = 40000 kWh Electricity Cost per kWh = $0.10 Air Conditioner A: COP_A = 2.3 Purchase and Installation Cost_A = $5500 Air Conditioner B: COP_B = 3.6 Purchase and Installation Cost_B = $7000 Now, we will calculate the annual running cost and total cost for each air conditioner: For Air Conditioner A: Energy Consumption_A = 40000 kWh / 2.3 = 17391.30 kWh Annual Running Cost_A = 17391.30 kWh * \(0.10 = \)1739.13 Total Cost_A = \(5500 + \)1739.13 = $7239.13 For Air Conditioner B: Energy Consumption_B = 40000 kWh / 3.6 = 11111.11 kWh Annual Running Cost_B = 11111.11 kWh * \(0.10 = \)1111.11 Total Cost_B = \(7000 + \)1111.11 = $8111.11

Comparison and Conclusion

Now we can compare the total costs: Total Cost_A = $7239.13 Total Cost_B = $8111.11 Since Total Cost_A < Total Cost_B, Air Conditioner A is a better buy considering the first-year cost.