Energy Units Math Challenge

Energy Challenge Math Problems – Answer Key

1. Kilowatt-hours = Watts x Hours / 1,000
   60 x 10 = 600
   600 / 1000 = 0.6 kWh
   
2. A kilowatt-hour represents one kilowatt of power used for one hour.
   2 x 3 = 6 kWh
   
3. 0.15 x 150 = $22.50
   
4. Work (J) = Force (N) x Distance (m)
   10 x 5 = 50 J
   
5. A calorie is equal to the energy needed to raise the temperature of 1 gram of water by 1°C.
   200 x 10 = 2000 calories
   
6. 100 x 5 = 500
   500 /1000 = 0.5 kWh
   
7. Energy (J) = Power (W) x Time (sec)
   1200 x 180 = 216,000 J
   
8. Potential Energy (J) = Mass (kg) x Gravity (9.8 m/s²) x Height (m)
   5 x 9.8 x 2 = 98 J
   
9. Energy (kWh) = Power (kW) x Time (hr)
   2000 x 24 = 48,000 kWh
   
10. Kinetic Energy (J) = ½ x Mass (kg) x v² (m/s)
    ½ x 2 = 1 and 4 x 4 = 16
    1 x 16 = 16 J
    
11. Work (J) = Force (N) x Distance (m)
    50 x 10 = 500 J
    
12. A kilocalorie is equal to 1,000 calories
    2.5 x 1000 = 2,500 cal
    
13. Energy (GWh) = Power (GW) x Time (hr)
    1 x 24 = 24 GWh
    
14. 15,000 x 3 = 45,000 BTU
    
15. 2 x 7 = 14
    14 x 100,000 = 1,400,000 BTU
    
16. One horsepower is approximately 746 watts.
    300 x 746 = 223,800 BTU
    
17. Work (ft-lb) = Force (lb) x Distance (ft)
    10 x 3 = 30 ft-lb
    
18. Energy (kWh) = Power (kW) x Time (hr)
    0.3 x 6 = 1.8 kWh

Energy Units Crossword Puzzle – Solution

Science of Coal

Computation
The Student Guide contains the Science of Coal – Computation activity.
Answer Key: Q1: China: [(4939 – 4883) / 4883] x 100 = 1.1%, India: [(1315 – 1245) / 1245] x 100 = 5.6%
Q2: ASEAN: [(491 – 457) / 457] x 100 = 7.4%
Q3: 2023: (457 / 8687) x 100 = 5.3%, 2027: (567 / 8873) x 100 = 6.4%
Q4: China: (9439 x 10⁹ kg) / (1.409 x 10⁹ people) = 3505 kg/person, India: (1315 x 10⁹ kg) / (1.451 x 10⁹ people) = 906 kg/person, U.S.: (368 x 10⁹ kg) / (340.1 x 10⁶ people) = 1082 kg/person
Q5: Use the formula: [(2027 value – 2023 value) / 2023 value] x 100 
China: 2.5%
India: 4.2% 
ASEAN: 24.1% 
U.S.: -14.2% 
EU: -31.1% 
Rest of World: -4.3%
Q6: 8873 Mt – 8687 Mt = +186 Mt increase

Data Set
The Student Guide contains the Science of Coal – Data Set.
Answer Key: Question 1: 1950 – United Kingdom; 2000 – United States; 2023 – China.
Question 2: Answers will vary. (Example: Countries that are currently developed like the U.K., U.S. and Germany, saw a steady rise in emissions through the industrial revolution into the 20th century, while currently developing countries, like China and India, did not start to increase their emissions until the late 20th century. In 2023, the UK, US and Germany have reached their peak emissions and have since shown steady decline, while China and India continue to steadily increase.)
Question 3: Answers will vary. (Example: The U.S. is a developed country and experienced rapid industrialization in the late 19th century and reached peak emissions in the early 20th century. It has since started transitioning away from coal in many sectors, toward natural gas and lower-emission energy options. China is a developing country and is still in its industrialization phase, starting its emissions increase in the late 20th century, close to one hundred years after the U.S. began increasing its coal emissions.)
Question 4: Answers will vary. (Example: Positive impacts include industrial growth that improves incomes and infrastructure. Negative impacts include worsening air pollution and higher greenhouse gas emissions.)
Question 5: Answers will vary. (Example: The United Kingdom was one of the first industrialized nations, so its coal use peaked early. Over time, the UK phased out coal in favor of oil, gas, nuclear and other lower-emission options.)

Science of Oil

Computation
The Student Guide contains the Science of Oil – Computation activity.
Answer Key: Q1: Cadillac: (1) 2400/20 = 120 gallons; (2) 120 x 20 = 2400 lbs; Mini Cooper: (1) 2400/30 = 80 gallons; (2) 80 x 20 = 1600 lbs; Hyundai Hybrid: (1) 2400/50 = 48 gallons; (2) 48 x 20 = 960 lbs.
Q2: Cadillac: (1) 120 x 3 = $360; (2) 360/5 = $72; Mini Cooper: (1) 80 x 3 = $240; (2) 240/5 = $48; Hyundai Sonata: (1) 48 x 3 = $144; (2) 144/5 = $28.80.
Q3: (1) 4.88 x 3 = 14.64 gallons/person
Q4: (1) 2400 x 53 = 127,200 lbs; (2) 127,200/160 = 795 lbs/person.
Q5: (1) Hyundai Hybrid; (2) Mini Cooper; (3) Cadillac; (4) Plane.
Q6: Answers will vary.

Data Set
The Student Guide contains the Science of Oil – Data Set.
Answer Key: Question 1: (Answers will vary) Example: Development of new technologies such as fracking and horizontal drilling; government incentives to increase energy independence and security.
Question 2: Example: Increased greenhouse gas emissions and water and land pollution; answers will vary. Question 3: Answers will vary.
Question 4: (Answers will vary) Example: Focus on other energy sectors and technologies.
Question 5: (Answers will vary) Example: The Middle East produces the most oil, followed by North America. The other regions have some big hitters, but trail behind in comparison.

Science of Natural Gas

Computation
The Student Guide contains the Science of Natural Gas – Computation activity.
Q1: Energy per day: 2400 ft² × 60 BTUs per ft² = 144,000 BTUs per day
Total energy over 90 days: 144,000 × 90 = 12,960,000 BTUs
12,960,000 BTUs / 1030 BTU per ft³ = 12,582.52 ft³
12,582.52 ft³ / 1000 = 12.58 mcf
Q2: Actual gas needed = energy needed / efficiency of furnace
12.58 mcf / 0.8 = 15.725 mcf
Cost = Actual gas needed × Cost per mcf
15.725 mcf × $6.00 per mcf = $94.35
Q3: 12.58 mcf / 0.9 = 13.98 mcf
13.98 mcf × $6.00 per mcf = $83.88
$94.35 – $83.88 = $10.47 (3 months) 
$10.47 × 4 = approximately $41.88 saved over a year

Data Set
The Student Guide contains the Science of Natural Gas – Data Set.
Answer Key: Question 1: Natural gas showed the most consistent increase in production from 2000 to 2023. Answers will vary. (Example: This consistency might be because many countries are investing in natural gas due to it being a better alternative (with regard to emissions) to coal in power plants. It’s also used in heating and industry, which keeps demand stable.)
Question 2: Between 2000 and 2023, coal had the largest absolute increase (49,789.16 TWh – 26,812.19 TWh = 22,976.97), way above oil and gas. Answers will vary. (Example: Coal’s large increase may be due to industrial growth in developing countries that still rely heavily on coal for electricity. It’s often cheaper and more available than other fuels.)
Question 3: Answers will vary.
Question 4: Natural gas shows a smoother and steadier growth line than coal and oil, but it is also the least produced of all three. While coal and oil had some drops (especially around 2020), natural gas didn’t dip much. At the same time, all three are trending up (increasing) overall, with oil being the most produced, followed by coal, then natural gas.
Question 5: Answers will vary. (Example: To support growing gas production, a country would need to invest in drilling technology and equipment, pipelines to transport the gas, storage facilities, and export terminals like liquefied natural gas (LNG) ports. They would also need safety and regulation systems, as well as new power plants that use natural gas efficiently, and expansion of their grid.)

Science of Nuclear

Computation
The Student Guide contains the Science of Nuclear – Computation activity.
Answer Key: Q1: 886 kWh/month x 12 months/year x 1.12 pounds coal/kWh = 11,900 pounds of coal
Q2: 886 kWh/month x 12 months/year x 1 MWh/1000 kWh x 0.007 pounds Uranium/MWh = 0.074 pounds of uranium
Q3: % difference = difference between values/average of values x 100
79,999,945 MJ/kg40,000,028 MJ/kg x 100 = 200%
Q4: % difference = difference between values/average of values x 100
39 MJ/kg35.5 MJ/kg x 100 = 110%
Q5: c) 10 grams
Explanation: 7,190 ÷ 5,730 = 3 half-lives
80 → 40 → 20 → 10 grams
Q6: c) 8 days
Explanation: 160 → 80 → 40 grams = 2 half-lives
16 days ÷ 2 = 8-day half-life
Q7: b) 3
Explanation: 10 → 5 → 2.5 → 1.25 → 3 halvings = 3 half-lives
Q8: c) 8 grams
Explanation: 13.5 ÷ 4.5 = 3 half-lives
64 → 32 → 16 → 8 grams

Data Set
The Student Guide contains the Science of Nuclear – Data Set.
Answer Key: Question 1: Germany’s nuclear power output declined after 2000 and dropped to 0 by 2023, showing a move away from nuclear energy. China rapidly increased its nuclear output, showing strong investment in nuclear for future energy needs.
Question 2: Answers will vary. (Example: Most U.S. reactors are old, and few new ones have been built due to high costs, long timelines, and stricter safety regulations.)
Question 3: Answers will vary. (Example: The Fukushima disaster in 2011 was a major nuclear accident caused by an earthquake, and it caused Japan to shut down many reactors and rethink its energy strategy for safety.
Question 4: Answers will vary. (Example: China is most likely to grow its nuclear share because of high demand for energy and government support for expanding nuclear energy.)
Question 5: Answers will vary. (Example: The global trend will likely lean toward expansion as countries seek low-carbon energy, though safety concerns and high cost will make this expansion slow.) 

Science of Wind

Computation
The Student Guide contains the Science of Wind – Computation activity.
Answer Key: Q1: (2304.44 – 345.92) / 13 = 150.66 TWh/year
Q2: 2020-2021 saw the largest increase of 258.79 TWh. Q3: (2304.44 / 29,429.05) = 0.783 = 7.83%
Q4: 2304.44 + (2 x 150.66) = 2605.76 TWh
Q5: (Answers will vary) Example: Falling costs of wind technology, government policies and subsidies, technological advancements, environmental concerns, energy security.

Data Set
The Student Guide contains the Science of Wind – Data Set.
Answer Key: Question 1: In the late afternoon/early evening (5 PM – 7 PM). This could be because people are returning home from work or school and turning on appliances, lights, electronics, etc. It’s also one of the hottest parts of the day, increasing cooling needs.
Question 2: No. Wind output is higher in the early morning hours and lower during the afternoon and evening, which is when electricity demand peaks.
Question 3: (Answers will vary) Example: Turbines can only generate near capacity when wind speeds are optimal; the wind may simply not be strong enough.
Question 4: (Answers will vary) Example: Geography and availability of water resources; cost of installation; fuel access; environmental impact.
Question 5: (Answers will vary) Example: Energy storage systems; complementary energy systems.

Science of Solar

Computation
The Student Guide contains the Science of Solar Computation activity.
Answer Key: Q1: (5000 watt/generator) x (1 panel/200 watt) = (5,000 panel/200 generators) = 25 panels/1 generator
Q2: A) Daily output per panel = 300 W × 5 h = 1,500 kWh = 1.5 kWh
Annual output = 1.5 kWh × 365 = 547.5 kWh
B) Number of panels = 900,000 kWh ÷ 547.5 kWh ≈ 1,644 panels
C) Improved output = 547.5 kWh × .20 = 109.5 kWh    547.5 kWh + 109.5 kWh = 657 kWh
Panels needed = 900,000 kWh ÷ 657 kWh/panel ≈ 1,370 panels
Panels saved = 1,645 panels  – 1,370 panels = 275 panels
Q3: A) Daily output per home = 6 kW × 4 h = 24 kWh
Annual output per home = 24 kWh × 365 = 8,760 kWh
Total annual output for 1,250 homes = 8,760 kWh × 1,250 homes = 10,950,000 kWh
B) Total CO₂ avoided = 10,950,000 kWh × 0.5 kg/kWh = 5,475,000 kgConvert to metric tons: 5,475,000 kg ÷ 1,000 = 5,475 metric tons CO₂ avoided annually

Data Set
The Student Guide contains the Science of Solar – Data Set.
Answer Key: Question 1: Total = 49.84 + 834.10 + 70.99 + 133.81 + 303.17 = 1391.91
China’s share = 834.10 ÷ 1391.91 ≈ 60%
Question 2: Answers will vary. (Example: Australia may have less developed solar infrastructure or lower energy demand due to its smaller population, while Germany has made significant investments and policies supporting solar energy, leading to higher production relative to its size.)
Question 3: Answers will vary. (Example: China’s far higher solar production suggests greater government investment, stronger policy incentives, or higher national energy demand compared to Australia.)
Question 4: Answers will vary. Question 5: Answers will vary.

Science of Hydropower

Computation
The Student Guide contains the Science of Hydropower – Computation activity.
Question 1: 12 million MWh x 0.80 = 9.6 million MWh 
Question 2: 15 million MWh x 0.90 = 13.5 million MWh of usable energy
Question 3: Yes. The region’s demand is 12 million MWh per year, and the dam is able to produce 13.5 million MWh per year. 13.5 million MWh – 12 million MWh = 1.5 million MWh excess power
Question 4: 13.5 million MWh x 1000 = 13,500,000,000 kWh
13,500,000,000 kWh / 10,000 = 1,350,000 homes
Question 5: Answers will vary. Student answers should be comprehensive and consider multiple factors including carbon dioxide emissions, cost, displacement of people and disruption of ecosystems, etc.

Data Set
The Student Guide contains the Science of Hydropower – Data Set.
Answer Key: Question 1: Between 1985 and 2023, China and Russia increased their share of hydroelectric power. China increased 2.3% (6.7 – 4.4) and Russia increased 1.1% (6 – 4.9).
Question 2: No, not necessarily. A decrease in the share of hydroelectric power doesn’t always mean a country is producing less of it. It could mean that the total energy demand has grown and other energy sources (such as fossil fuels or solar, nuclear and wind) have increased even faster. So the hydroelectric output might be the same or even higher, but its percentage of the total energy mix has gone down.
Question 3: Answers will vary. (Example: Positive impacts include (environmental) reduced greenhouse gas production, cleaner air quality, less acid rain and (economic) job creation, lower long-term cost of operation, less damage from flooding. Negative impacts include (environmental) disruption of habitats/ecosystems, increased sedimentation, increased methane production in tropical regions due to the breakdown of organic material and (economic) high initial costs, displacing communities.
Question 4: Answers will vary. (Example: Countries may be focusing on developing and innovating other low-emission energy sources, such as wind and solar. Hydropower has been used for many years and is a stable energy source limited by the geography and availability of moving water.)
Question 5: Answers will vary. (Example: Norway has abundant mountainous terrain and steep rivers, making it ideal for building hydroelectric dams. Norway is also a wealthy nation that adopted hydropower early and has consistently maintained their dam systems. There is strong political commitment to sustainability and energy independence, with policies that support state-owned hydro companies and investment in sustainable energy.)

Science of Geothermal

Computation
The Student Guide contains the Science of Geothermal – Computation activity.
Answer Key: Q1: Energy (MWh) = Power (MW) x Time (hours)
35 MW x 24 hours = 840 MWh
Q2: Monthly Savings: 2,000 kWh – 800 kWh = 1,200 kWh
Yearly Savings: 1,200 kWh x 12 months = 14,400 kWh
Q3: Monthly Savings: $200 – $90 = $110
$110 x 12 months = $1,320
Q4: $20,000 / $1,500 per year = 13.3 years
Q5: Conventional System: $10,000 + ($2,000 x 10) = $30,000
Geothermal System: $20,000 + ($700 x 10) = $27,000
Answer: Geothermal is cheaper by $3,000 after 10 years.

Data Set
The Student Guide contains the Science of Geothermal – Data Set.
Answer Key: Question 1: Answers will vary. (Example: Countries like Türkiye, Kenya, Indonesia and Iceland made geothermal energy a national priority. The evidence is in their massive energy increases: Türkiye grew by 9,535%, Kenya by 1,530%, Indonesia by 403%, and Iceland by 385%. These huge jumps showed that they invested heavily in geothermal projects in a short period of time.
Question 2: Explanations may vary. (Example: Japan shows the biggest decrease, a drop of -8%. This suggests that Japan may have shifted away from geothermal energy to other energy sources, or faced challenges like high costs, land limitations, or environmental concerns that slowed geothermal growth.)
Question 3: Answers will vary. (Example: Mexico, Italy, and China expanded their capacity slowly but steadily. Mexico grew by 18%, Italy by 31%, and China by 19%. This suggests that they see geothermal as useful but not their main energy focus. They may be balancing this growth with growth of other energy sources.
Question 4: Answers will vary. (Example: Both Indonesia and Türkiye look like future global leaders. Indonesia has the higher total capacity at 2,639 MW, showing it already plays a major role. But Türkiye’s 9,535% growth shows it is catching up fast and putting enormous focus on geothermal energy. Both countries seem to have the resources and government support to expand further.)
Question 5: Explanations may vary. (Example: The Philippines had a surprisingly small increase – only 6%. This might be because it already had such a large geothermal base in 2000, so there wasn’t much room to expand. It could also mean the country is focused on maintaining existing plants rather than building new ones, or that it turned to other energy sources to balance its energy mix.)

Science of Biofuels

Computation
The Student Guide contains the Science of Biofuels – Computation activity.
Answer Key: Q1: (1) Calculate the land required by the traditional process: 0.045 acres/gallon x 10,000 gallons = 450 acres
(2) Calculate the land required by the new process: 0.038 acres per gallon x 10,000 gallons = 380 acres
(3) Calculate the difference in land use: 450 acres – 380 acres = 70 acres
Answer: The facility would save70 acres of land by using the new process instead of the traditional one.
Q2: (1) Convert current water usage to liters: 8,500,000 cubic meters x 1,000 = 8,500,000,000 liters.
(2) Calculate water savings: 8,500,000,000 x 0.25 = 2,125,000,000 liters.
Answer: By converting to switchgrass, they would save 2.125 billion liters of water annually.
Q3: (1) Calculate the total biomass harvested: 15 acres x 5 tons per acre = 75 tons of biomass
(2) Calculate the total gallons of ethanol produced: 75 tons x 80 gallons per ton = 6,000 gallons of ethanol
(3) Calculate the total BTUs produced: 6,000 gallons x 76,330 BTUs per gallon = 457,980,000 BTUs
Answer: The total BTUs of energy that can be produced from this harvest is 457,980,000 BTUs.
Q4: (1) Calculate that total energy content of the desired petroleum diesel: 100,000 gallons x 138,000 BTUs per gallon = 13,800,000,000 BTUs
(2) Determine the total gallons of switchgrass biofuel needed: 13,800,000,000 BTUs (target energy) / 76,330 BTUs/gallon = approximately 180,794 gallons of switchgrass ethanol
(3) Calculate the tons of switchgrass biomass needed: 180,794 gallons (biofuel needed) / 80 gallons per ton = approximately 2,260 tons of switchgrass biomass
(4) Calculate the acres of switchgrass needed: 2,260 tons (biomass needed) / 5 tons per acre = approximately 452 acres
Answer: Approximately 452 acres of switchgrass would be needed to match the energy content of 100,000 gallons of petroleum diesel

Data Set
The Student Guide contains the Science of Biofuels – Data Set.
Answer Key: Question 1: Answers will vary. (Example: Both the United States and Brazil have large agricultural industries that make biofuel production easier. The U.S. grows a lot of corn, and Brazil grows a lot of sugarcane, which are very efficient crops for making ethanol. Both countries also have policies that encourage research into the production of biofuels and promote biofuels as a way to lower carbon emissions. Economically, biofuels also provide jobs in farming and energy production.)
Question 2: Answers will vary. (Example: Indonesia’s biofuel production may have grown more quickly because its government placed a stronger focus on developing this energy source. China, on the other hand, may have decided to invest more heavily in other energy sources instead. Also, Indonesia may have more flexibility to use land and resources for producing biofuels.)
Question 3: Answers will vary. (Example: China and India both have to focus on providing reliable energy for and providing food for their very large populations. Using farmland to grow crops for fuel might take away from food production, so they may not want to rely heavily on biofuels. They also may have limited resources like water and arable land, and have focused on other types of energy that are better long-term options.)
Question 4: Answers will vary.
Question 5: Answers will vary. 

Science of Energy Efficiency

Computation
The Student Guide contains the Science of Energy Efficiency – Computation activity.
Answer Key: Q1: 60W x 5hr = 300Wh per day
Q2: 10W x 5hr = 50Wh per day
Q3: 300Wh – 50Wh = 250Wh saved per day
Q4: 250Wh / 1,000 = 0.25kWh
0.25kWh per day x 30 days = 7.5kWh
7.5kWh x $0.17 = $1.28 saved per month
Q5: $1.28 x 12 months = $15.36
$15.36 x 40 = $614.40 saved per year

Data Set
The Student Guide contains the Science of Energy Efficiency – Data Set.
Answer Key: Question 1: (Sample Student Response: Overall, residential energy intensity in the United States decreases from 2000 to 2023 for most household uses. This suggests that homes are providing the same services while using less energy, likely because of improvements in energy efficiency. Better appliances, improved building design, and newer technologies allow households to heat, cool, and power homes more efficiently than in the past.)
Question 2: (Sample Student Response: One use that does not follow the general decreasing pattern as clearly is space cooling. Its energy intensity does not drop as much as other categories. A possible explanation is that more homes now use air conditioning, especially in warmer regions, and people may cool their homes more often or to lower temperatures. Climate change and rising average temperatures could also increase the demand for cooling, offsetting efficiency improvements.
Question 3: (Sample Student Response: Space heating shows a clear decrease in energy intensity from 2000 to 2023. This change can be explained by improvements in home insulation, windows, and heating systems. The graph shows that space heating drops significantly over time, indicating that efficiency improvements in buildings and heating technology have had a major impact.
Lighting also shows a noticeable decrease in energy intensity. This is likely due to the widespread use of LED and other types of energy-efficient light bulbs, which use much less energy than traditional incandescent light bulbs while providing the same or better light.)
Question 4: (Sample Student Response: Total residential energy use could still increase even if energy intensity is decreasing because there may be more homes or larger homes over time. If the number of households increases, the total energy used can go up, even if each home is using energy more efficiently. People may also use more energy services, such as owning more appliances or using air conditioning more often.)

Science of Energy Storage

Computation
The Student Guide contains the Science of Energy Storage – Computation activity.
Answer Key: Q1: Pumped Storage Hydropower ($0.022/kWh) and Compressed Air Energy Storage ($0.026/kWh)
Q2: Pumped Storage Hydropower (85% reduction) and Lead Acid Batteries (77% reduction)
Q3: EDLC Supercapacitors (5.5 years) and Zinc Batteries (6 years)
Q4: LCOS = $0.082/kWh; Calculation: 500,000 × 0.082 = $41,000
Q5: Zinc duration = 6 years, Sodium-ion = 11 years; Calculation: 11 – 6 = 5 years
Q6: LIBs cost = $1,063M, PbAs = $176M; Calculation: 1,063 – 176 = $887 million
Q7: LCOS = $0.086/kWh; Calculation: 1,000,000 × 0.086 = $86,000
Q8: Final = Original × (1 – 0.51); 0.070 = Original × 0.49; Original = 0.070 / 0.49 = $0.143/kWh
Q9: Final = Original × 0.76; 0.337 = Original × 0.76; Original = 0.337 / 0.76 = $0.443/kWh
Q10: LIBs = $0.070, Zinc = $0.082, Sodium-ion = $0.255 Answer: LIBs < Zinc < Sodium-ion

Data Set
The Student Guide contains the Science of Energy Storage – Data Set.
Answer Key: Question 1: Answers will vary. (Example: Before 2010, the growth in energy installations was slow, and after around 2015, there was much faster growth. This rapid increase could be due to falling battery costs, improved technology, and growing demand for storage to support low-emissions energy like solar and wind. Government incentives and climate priorities might also have helped.)
Question 2: Answers will vary. (Example: Some storage projects may not have detailed technology available – especially older projects, international entries, or ones from private companies that didn’t report specifics. This makes it harder to know which storage types are most commonly used or growing fastest. It limits our ability to understand trends by technology and makes it harder to plan for future needs.)
Question 3: Answers will vary. (Example: The increase in energy storage installations likely reflects the growing need to store energy from solar and wind so it can be used when the sun isn’t shining or the wind isn’t blowing. Storage helps balance the energy supply and demand, making wind and solar energy more reliable. The rising trend suggests that energy storage is becoming a key part of electricity systems with variable generation.
Question 4: Answers will vary. (Example: Challenges might include shortages of materials like lithium or cobalt used in batteries, which can drive up costs. There may also be issues with safely recycling or disposing of used batteries. On the grid side, adding lots of storage capacity requires updates in infrastructure, and smart control systems to manage it effectively.)
Question 5: Answers will vary. (Example: Different technologies are good for different tasks. For example, lithium-ion batteries are great for short-term energy use, while pumped hydro can store large amounts for longer periods. If we relied on only one type, we might run into problems with cost, material shortages, or technical limitations. A diverse mix makes the system more flexible, resilient, and able to meet different kinds of energy needs.)

Science of Electricity

Computation
The Student Guide contains the Science of Electricity – Computation activity.
Answer Key: Q1: 150,000,000 kWh / 0.33 = 454,545,455 million kWh
454,545,455 kWh / 293 = 1,551,350 MMBtu
Q2: 150,000,000 million kWh × $0.0220 = $3,300,000
Q3: Coal: 0.74 lb per kWh x 150,000,000 kWh = 111,000,000 lbs
Natural Gas: 0.40 lb per kWh x 150,000,000 kWh = 60,000,000 lbs
111,000,000 – 60,000,000 = 51,000,000 lbs of CO₂ (coal emits that much more than natural gas)
Q4: Nuclear: 0.50 x 150,000,000 kWh = 75,000,000 kWh
Hydropower: 0.30 x 150,000,000 kWh = 45,000,000 kWh
Solar: 0.20 x 150,000,000 kWh = 30,000,000 kWh
Q5: Nuclear: 75,000,000 kWh x 0.02219 = $1,664,250
Hydropower: 45,000,000 x 0.01471 = $661,950
Solar: 30,000,000 x 0.02647 = $794,100
Total: $1,664,250 + 661,950 + 794,100 = $3,120,300
Q6: (0.50 x 0.2219) + (0.30 x 0.01471) + (0.20 x 0.02647) = $0.020802 ($0.021/kWh)

Data Set
The Student Guide contains the Science of Electricity – Data Set.
Answer Key: Question 1: Answers will vary. (Example: Many countries still rely on existing coal infrastructure; it’s relatively cheap and abundant, and transitioning takes time and investment.)
Question 2: Answers will vary. (Example: Wind and solar are newer technologies, require high upfront costs, depend on weather conditions, and may lack sufficient grid or storage support.)
Question 3: Answers will vary. (Example: Coal, oil, and nuclear have declined. Reasons may include environmental concerns, decommissioning of old plants, safety concerns (especially nuclear), and competition from cheaper sources, or sources with lower emissions.)
Question 4: Answers will vary. (Example: Likely wind or solar, due to falling costs, international climate goals, and improved technologies of solar panels and/or wind turbines, and energy storage capacity.)
Question 5: Answers will vary. (Example: Economically, some sources are cheaper or subsidized. Politically, countries may want energy independence or to meet international agreements. Environmentally, there’s pressure to reduce emissions and pollution.)

Science of the Electric Grid

Computation
The Student Guide contains the Science of the Electric Grid – Computation activity.
Answer Key: Q1: 40 panels x 300W = 12,000W
Q2: 12,000W = 12kW; 12kW x 5 hours = 60kWh
Q3: Yes. The microgrid produces 60kWh per day, which is 5kWh more than the village needs (55kWh per day).
Q4: Step 1: Find the Energy Shortfall: 75kWh (needed) – 60kWh (produced) = 15kWh
Step 2: Find Daily Energy Produced by One Panel: 300W x 0.3kW; 0.3kW x 5h = 1.5kWh/day
Step 3: Divide Shortfall by Energy per Panel: 15kWh/1.5kWh = 10 panels

Data Set
The Student Guide contains the Science of the Electric Grid – Data Set.
Answer Key: (Answers will vary: Key ideas included)
Question 1: Greatest variability: Solar (large daily swings; zero at night); Wind (changes with weather partners and wind speed); Solar and wind depend on weather and time of day, so their output naturally fluctuates. Medium variability: Natural gas and Hydro (rises and falls to match changing demand). Natural gas plants can ramp up and down quickly, making them “flexible” and well-suited to fill gaps. Hydro is dispatchable to a degree; operators can adjust water flow through turbines, but it is still constrained by limits like river flow and reservoir rates. Most constant (steady baseline generation): Nuclear and Coal; Nuclear and coal plants are designed to run continuously at stable levels. They operate best at steady output and are not typically adjusted hour to hour.
Question 2: Operators must ensure other power sources are available early in the morning before solar ramps up and in the evening when solar rapidly drops (the “duck curve” problem). They need sufficient flexible backup generation, such as natural gas or hydropower, to fill in during non-sunlight hours. Increased solar may require energy storage, demand shifting, or improved forecasting to manage the steep rises and drops. Solar’s predictable daily pattern helps planning, but its variability still requires careful coordination.
Question 3: When wind production rises, natural gas generation often decreases, meaning gas plants reduce output because wind is providing more electricity. When wind drops, natural gas ramps up, covering the shortfall. This shows that natural gas plants act as a balancing or “dispatchable” resource, filling in the gaps left by variable wind output. It also shows how fossil-fuel plants currently provide the flexibility needed to integrate more renewable energy into the grid.
Question 4: Large-scale battery storage would smooth out the ups and downs in natural gas production. Batteries could store excess renewable energy and release it when solar or wind drop, reducing the need for natural gas to ramp up quickly. As a result, natural gas would show fewer spikes, and overall usage might decrease.
Question 5: Answers will vary. Examples include: Times of peak electricity demand; how quickly different sources ramp up or down (solar in the evening, wind changes, etc.); which sources are predictable and which are variable; availability of flexible generation (like natural gas); patterns of renewable production and when backup power will be needed; potential mismatches between supply and demand; forecastable trends (daily solar cycles, expected wind patterns); forecastable trends (daily solar cycles, expected wind patterns).
Question 6: The graph shows constant movement, with some sources rising while others fall. Demand fluctuates hourly, and renewable output is not perfectly aligned with these changes. Operators must continuously adjust which plants are running to keep supply exactly equal to demand every moment. Renewable variability means the system must have fast, flexible resources ready to respond. The need to coordinate many sources with different behaviors (steady, variable, ramping) highlights the complexity of maintaining a stable, reliable grid.