Many electric companies use time-of-day pricing in which electricity costs more during hours of high demand. Suppose electricity costs \$0.21/kWh from 10 a.m. to 6 p.m.; \$0.09/kWh at all other times. What is the annual cost of electricity for a 2.5 kW industrial pump that runs 24 hours a day?

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Determine the total energy consumption of the industrial pump in a single day. Since the pump runs 24 hours a day and has a power rating of 2.5 kW, the daily energy consumption is calculated as: $ E_{\text{daily}} = P \times t $, where $ P = 2.5 \; \text{kW} $ and $ t = 24 \; \text{hours} $.

Split the daily energy consumption into two time periods: (1) from 10 a.m. to 6 p.m. (8 hours) and (2) the remaining 16 hours. For the first period, calculate the energy consumed as $ E_{\text{peak}} = P \times t_{\text{peak}} $, where $ t_{\text{peak}} = 8 \; \text{hours} $. For the second period, calculate the energy consumed as $ E_{\text{off-peak}} = P \times t_{\text{off-peak}} $, where $ t_{\text{off-peak}} = 16 \; \text{hours} $.

Calculate the daily cost of electricity for each time period. For the peak period, the cost is $ C_{\text{peak}} = E_{\text{peak}} \times \text{rate}_{\text{peak}} $, where $ \text{rate}_{\text{peak}} = 0.21 \; \text{ extdollar/kWh} $. For the off-peak period, the cost is $ C_{\text{off-peak}} = E_{\text{off-peak}} \times \text{rate}_{\text{off-peak}} $, where $ \text{rate}_{\text{off-peak}} = 0.09 \; \text{ extdollar/kWh} $.

Add the costs from the two time periods to find the total daily cost of electricity: $ C_{\text{daily}} = C_{\text{peak}} + C_{\text{off-peak}} $.

Multiply the daily cost by the number of days in a year (365) to find the annual cost of electricity: $ C_{\text{annual}} = C_{\text{daily}} \times 365 $.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Power and Energy

Power is the rate at which energy is consumed or produced, measured in watts (W). Energy, measured in kilowatt-hours (kWh), is the total amount of power used over time. To calculate energy consumption, multiply the power rating of an appliance by the time it operates. In this case, the industrial pump's power rating of 2.5 kW indicates it consumes 2.5 kWh for every hour of operation.

Time-of-Day Pricing

Time-of-day pricing is a billing strategy used by electric companies where the cost of electricity varies based on the time it is consumed. During peak hours, when demand is high, prices are elevated to encourage users to reduce consumption. Conversely, during off-peak hours, prices are lower to incentivize usage. Understanding this pricing model is essential for calculating the total cost of electricity based on the pump's operating schedule.

Annual Cost Calculation

To determine the annual cost of electricity, one must calculate the total energy consumed during both peak and off-peak hours and then multiply by the respective rates. This involves determining how many hours the pump operates during each pricing period over a year. The annual cost is the sum of the costs incurred during peak and off-peak times, providing a comprehensive view of the electricity expenses for the industrial pump.