Lesson 20: Fossil Fuels & Nuclear Energy

Warm-Up

A lump of coal is stored sunlight — energy captured by plants in an ancient swamp, buried and cooked for 300 million years. When we burn it, we release that energy (and its carbon) in seconds. Nuclear energy taps a totally different reservoir: the binding energy inside atomic nuclei, split apart to boil water with no carbon at all — but with radioactive waste that stays dangerous for millennia. This lesson covers the workhorses of the power grid: the three fossil fuels and nuclear fission. It's also where half-life math lives, a guaranteed calculation. The recurring theme is trade-offs: cheap and reliable vs. carbon, safety, and waste.

Core Concept

How fossil fuels form and generate power

All fossil fuels form from ancient organic matter buried under heat and pressure over millions of years: - Coal — from ancient plants in swamps; a solid. Ranked by carbon content (lignite → bituminous → anthracite); highest energy and cleanest-burning is anthracite. - Oil (petroleum) — from ancient marine organisms; a liquid, refined into gasoline, diesel, etc. - Natural gas (mostly methane, CH₄) — often found with oil; a gas.

Electricity from fossil fuels works by combustion → heat → steam → turbine → generator:

[DIAGRAM: Fossil-fuel (thermal) power plant. Fuel burned in a boiler → heat boils water → high-pressure steam spins a turbine → turbine turns a generator → electricity. Cooling water condenses steam (cooling tower/river). Emissions (CO₂, SO₂, NOₓ, particulates) exit the smokestack.]

Comparing the three: - Coal — most abundant, cheapest, but dirtiest: highest CO₂ per unit energy, plus SO₂ (acid rain), NOₓ, particulates, mercury, and ash. Mining impacts (Lesson 17). - Oil — energy-dense, portable → dominates transportation; spills (Deepwater Horizon), CO₂, air pollution. - Natural gas — cleanest fossil fuel: ~half the CO₂ of coal per unit energy, fewer other pollutants. But extraction via hydraulic fracturing (fracking) can contaminate groundwater, cause induced earthquakes, and leak methane (a potent greenhouse gas).

Extraction: conventional drilling/mining plus unconventional methods — fracking (injecting high-pressure fluid to crack shale and release gas/oil), tar sands, and offshore drilling — each with added environmental risk.

Nuclear energy

Nuclear power uses nuclear fission: a neutron splits a uranium-235 (or plutonium) nucleus, releasing energy and more neutrons that split further nuclei — a controlled chain reaction. The heat boils water to steam, driving a turbine (same turbine-generator step as fossil plants), but with no combustion and no CO₂.

[DIAGRAM: Nuclear reactor core. Fuel rods (U-235) + control rods (absorb neutrons to regulate the chain reaction) + moderator (water, slows neutrons) + coolant. Heat → steam generator → turbine → generator → electricity. Containment structure surrounds the core.]

Reactor components: - Fuel rods — enriched uranium. - Control rods — absorb neutrons to speed up/slow the reaction (fully inserted = shutdown). - Moderator (often water) — slows neutrons so fission continues. - Coolant — removes heat; loss of coolant risks meltdown. - Containment building — shields against radiation release.

Advantages: no CO₂ or air pollution during operation, high energy density, reliable baseload power.

Disadvantages/risks: - Radioactive waste — spent fuel stays dangerous for thousands of years; long-term storage (e.g., deep geologic repositories) is unresolved. - Accidents — Chernobyl (1986, Ukraine): reactor explosion/fire, major radiation release; Fukushima (2011, Japan): tsunami knocked out cooling → meltdowns; Three Mile Island (1979, US): partial meltdown, limited release. - Thermal pollution — warm cooling water discharged to rivers/lakes. - High cost and long build times; uranium mining impacts; weapons-proliferation concerns.

Half-life and radioactive decay

Half-life is the time for half of a radioactive sample to decay. After each half-life, the remaining amount halves: remaining = initial × (½)^(number of half-lives), where number of half-lives = elapsed time ÷ half-life.

This governs how long nuclear waste stays hazardous and is a guaranteed calculation.

Cogeneration

Cogeneration (combined heat and power, CHP) captures the "waste" heat from electricity generation and uses it for heating, raising overall efficiency from ~30–35% to ~80%. A key efficiency solution (Lesson 22).

Why this matters

Comparing fossil fuels by emissions, describing the shared turbine-generator mechanism, explaining nuclear components and famous accidents, and computing half-lives are all frequent exam tasks. This lesson also seeds Unit 7 (combustion pollutants) and Unit 9 (CO₂/methane).

Worked Examples

Example 1 (easy): Rank fossil fuels by CO₂

Rank coal, oil, and natural gas from most to least CO₂ emitted per unit energy.

Solution: Coal > oil > natural gas. Coal emits the most CO₂ (and other pollutants) per unit energy; natural gas emits about half of coal's CO₂ and is the cleanest fossil fuel.

Interpretation: Natural gas is the "cleanest" fossil fuel; coal the dirtiest.

Example 2 (medium): Reactor components

What is the role of control rods, and what happens when they are fully inserted?

Solution: Control rods absorb neutrons, regulating the fission chain reaction. Inserting them further slows the reaction (fewer neutrons available to split nuclei); fully inserted, they absorb enough neutrons to stop the chain reaction — a shutdown.

Interpretation: Control rods = neutron absorbers = the reactor's throttle/brake.

Example 3 (AP-style): Half-life calculation

A radioactive isotope has a half-life of 30 years. Starting with 80 grams, how much remains after 90 years?

Strategy: half-lives = 90 ÷ 30 = 3; halve three times.

Solution:

Number of half-lives = 90 / 30 = 3
80 → 40 (30 yr) → 20 (60 yr) → 10 (90 yr)
Or: 80 × (½)^3 = 80 × 1/8 = 10 g

Answer: 10 grams remain.

Interpretation: Each half-life halves the amount; count the half-lives, then halve that many times.

Example 4 (AP-style): Fracking trade-off

Natural gas is promoted as a "cleaner" fuel. Give one climate benefit and two environmental concerns of obtaining it via fracking.

Solution: Benefit: burning natural gas emits about half the CO₂ of coal per unit energy, lowering emissions if it replaces coal. Concerns: (1) methane leakage during extraction — methane is a potent greenhouse gas that can offset the CO₂ benefit; (2) groundwater contamination from fracking fluids (also induced earthquakes, high water use).

Interpretation: Lower combustion CO₂, but extraction (methane leaks, water risks) complicates the "clean" label.

Common Mistakes

• Thinking nuclear "burns" fuel or emits CO₂. Nuclear uses fission, not combustion — no CO₂ during operation. (Its issue is waste and accidents.)
• Botching half-life math. Divide elapsed time by half-life to get the number of half-lives, then halve repeatedly. Don't subtract.
• Calling natural gas carbon-free. It's the cleanest fossil fuel (~half coal's CO₂), not zero-carbon — and methane leaks matter.
• Confusing control rods and fuel rods. Fuel rods (uranium) provide fissile material; control rods (neutron absorbers) regulate the reaction.
• Forgetting the shared mechanism. Coal, gas, nuclear, and geothermal all ultimately boil water to spin a turbine; the difference is the heat source.

Practice Problems

11. (FRQ-style) Compare a coal plant and a nuclear plant in terms of CO₂ emissions, air pollution, fuel renewability, and waste. Note one shared mechanism.

12. (Math) Nuclear waste isotope has a half-life of 24,000 years, starting at 64 kg. (a) How much remains after 72,000 years? (b) Explain why this makes disposal challenging.

FRQ Practice — Analyze an Environmental Problem and Propose a Solution with Calculations (10 pts)

A utility is deciding between expanding a coal plant or building a nuclear plant. A radioactive byproduct of the nuclear option has a half-life of 30 years.

(a) State two environmental advantages of nuclear over coal. (2 pts) (b) State two disadvantages/risks of the nuclear option. (2 pts) (c) A 90 kg sample of the byproduct decays with a 30-year half-life. Calculate how much remains after 120 years. Show work. (3 pts) (d) Recommend one option and justify your choice, addressing both climate and waste. (3 pts)