A 15,000-square-foot commercial office building uses 35,000 kWh per month and has a peak demand of 150 kW. Estimate the monthly electric bill and the annual electric cost.
The correct answer and explanation is:
To estimate the monthly electric bill and the annual electric cost, we need to take into account both the energy consumption (measured in kilowatt-hours, kWh) and the demand charges (measured in kilowatts, kW).
Monthly Electric Bill
For many commercial buildings, the electric bill consists of two major components:
- Energy Charges: These are based on the total energy consumed, usually priced per kWh.
- Demand Charges: These are based on the peak demand in kilowatts, typically charged at a fixed rate per kW.
We can estimate the total electric bill using the following steps:
- Energy Charges:
The building uses 35,000 kWh per month. Assuming an average cost of $0.10 per kWh for energy usage: Energy Charge=35,000 kWh×0.10 USD/kWh=3,500 USD/month\text{Energy Charge} = 35,000 \, \text{kWh} \times 0.10 \, \text{USD/kWh} = 3,500 \, \text{USD/month} - Demand Charges:
The building has a peak demand of 150 kW. Assuming the demand charge is $15 per kW per month: Demand Charge=150 kW×15 USD/kW=2,250 USD/month\text{Demand Charge} = 150 \, \text{kW} \times 15 \, \text{USD/kW} = 2,250 \, \text{USD/month}
Thus, the monthly electric bill is the sum of these two charges: Monthly Bill=3,500 USD+2,250 USD=5,750 USD/month\text{Monthly Bill} = 3,500 \, \text{USD} + 2,250 \, \text{USD} = 5,750 \, \text{USD/month}
Annual Electric Cost
To find the annual cost, we multiply the monthly electric bill by 12: Annual Electric Cost=5,750 USD/month×12 months=69,000 USD/year\text{Annual Electric Cost} = 5,750 \, \text{USD/month} \times 12 \, \text{months} = 69,000 \, \text{USD/year}
Summary
- Monthly Electric Bill: $5,750
- Annual Electric Cost: $69,000
This estimate assumes average rates for energy and demand charges. Actual rates may vary based on the utility provider, location, and other factors.