This activity explores how efficiently different energy sources produce electricity, using real-world data. You will calculate energy outputs, fuel requirements, costs, and environmental impacts using a mix of math skills.

Reference Table

Column 2: Typical Performance Metric (%)

For power plants that burn fuels such as coal, natural gas, or nuclear fuel, the performance metric shown is thermal efficiency. This means the percentage of the fuel’s heat energy that is successfully converted into electricity (for example, 33% efficiency means only one-third of the heat energy becomes electricity, while the rest is lost as heat). For zero-fuel sources like hydropower, wind, and solar, the performance metric shown is the capacity factor. This represents the average percentage of time a plant produces electricity at its maximum output over a year (for example, a 35% capacity factor means the plant generates about one-third of the electricity it could if it ran at full power all the time, because the sun doesn’t always shine and the wind doesn’t always blow).

Column 3: Power Plant Operation Cost per kWh Produced ($)

This value represents the average cost of producing one kilowatt-hour (kWh) of electricity, combining three main power plant expense categories: operation, maintenance, and fuel. For example, it costs an average of $0.0220 (or 2.2 cents) for a coal power plant to generate one kilowatt-hour of electricity.

Instructions: Study the reference table above to answer the computational questions. 

Q1. Assume a city requires 150 million kWh of electricity per year. How many MMBTUs (million BTUs) are required to generate 150 million kWh using a coal plant that is 33% efficient? Show your work and round your answer to the nearest whole number.

Q2. Using the table’s operation cost for coal, what is the annual operation cost to supply 150 million kWh? Show your work.

Q3. How many pounds of CO₂ would be emitted by coal vs. natural gas to produce 150 million kWh of electricity? What is the difference? Show your work.

Q4. If the city gets 50% of its electricity from nuclear, 30% from hydropower, and 20% from solar, how many kWh does each source provide? Show your work.

Q5. Using the table’s operation costs ($/kWh), compute the annual operation cost for each source listed in Question 4 and the total. Show your work.

Q6. What is the weighted-average operation cost ($/kWh) of the portfolio from Questions 4-5? Show your work and round your answer to the nearest thousandth.)
Note: A weighted average accounts for how much each part contributes to the whole. Multiply each category’s value by its share (its “weight”), then add them up. The weights should sum to 1 (or 100%). Here, each source’s cost per kWh is weighted by the percentage of total electricity it provides.