This unit is ≈4% of the A-Level Physics, across 8 lessons. Full syllabus
Lesson 7 of 8 · Options and board-specific extensions
Energy and the environment
9 min read · about 55 min with practice3 quick checks<1% of the testCore: Core: tested on most papers
Reading is free. Sign in to tick off lessons, keep your place and track your mastery.
This is Option D for Eduqas (Component 3, Section B) and WJEC (Unit 4, Section B). It is worth 20 marks, usually set as one or two structured questions. They mix quick calculations (wind power, hydro, solar intensity, U-values) with an explain or evaluate part on the greenhouse effect, fusion or fuel cells. The physics is mostly AS-level, used carefully in context, so accuracy and precise explanations win the marks.
By the end you’ll be able to
Model the Earth’s energy balance using Stefan’s law and explain the greenhouse effect
Calculate power available from wind (½ρAv³) and water (flow rate × ρgh) and efficiency of solar cells
Use thermal conduction ΔQ/Δt = −AK ΔT/Δx and U-values for building insulation
Evaluate fuel cells, batteries and pumped storage and the environmental impacts of each energy source
What the exam asks
Earth’s energy balance: radiation in from the Sun must equal radiation out; the greenhouse effect and CO₂; Wien’s law and Stefan’s law for the Sun and the Earth; why melting land ice raises sea level but melting icebergs do not.
Solar: the proton–proton chain, the inverse square law I=4πd2P, and photovoltaic efficiency.
Wind, hydro, tidal and pumped storage: ; energy and power from falling water; comparisons between sources.
vii.Check your understanding
3 questions on energy and the environment. Every option is explained once you answer.
Sign in to try the quick check
Answers are checked on our side, every option is explained, and your result feeds your mastery for this topic. It’s free.
The first 3 of 9 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.
PromptCard 1 of 3
Write the Earth’s radiative equilibrium equation.
P=21ρAv3
Nuclear: enrichment and breeding in fission; why sustained fusion is hard (the triple product).
Fuel cells, and thermal conductionΔtΔQ=−AKΔxΔθ with U-values, rate =UAΔθ.
Core ideas
The Earth’s energy balance and the greenhouse effect
The Sun is a black body at about 5800 K, powered by the proton–proton chain (four protons fuse to form helium-4, two positrons and two neutrinos, releasing 26.7 MeV). Its spectrum peaks at λmax=58002.90×10−3=500 nm, in the visible. The energy crosses empty space as electromagnetic radiation, and its intensity falls with the inverse square law. At the Earth it is about 1.36 kW m⁻² (the solar constant).
In thermal equilibrium, the power absorbed equals the power radiated. The Earth intercepts sunlight over a disc, πR2, but radiates from its whole surface, 4πR2. About 30% of the incoming sunlight is reflected (the albedo, a≈0.30). So
S(1−a)πR2=σ(4πR2)T4⇒T=(4σS(1−a))1/4≈255K
The real mean surface temperature is about 288 K. The difference is the greenhouse effect. The Earth radiates in the infrared, at λmax≈2882.90×10−3≈10 µm. The atmosphere is largely transparent to the incoming visible and near-infrared light, but CO₂, water vapour and methane absorb this outgoing infrared and re-emit it in all directions, partly back towards the ground. More CO₂ means more of the outgoing radiation is absorbed. Less then escapes to space, so the Earth is out of balance and warms until it radiates enough to restore equilibrium at a higher temperature. The waste heat from humanity’s direct energy use (about 2×1013 W) is only about 10−4 of the solar input, so the warming comes from the CO₂ produced by burning fuels, not from the heat released directly.
Sea level (Archimedes): floating ice displaces its own weight of water. When it melts, the meltwater exactly fills the volume it displaced, so melting icebergs and sea ice do not raise the sea level. Ice on land (Greenland, Antarctica, glaciers) adds new water to the oceans, so it does raise the sea level. The thermal expansion of warming seawater raises it too.
Solar, wind, water
Photovoltaic efficiency=intensity×areaelectrical power out, typically 15–22%.
Wind: the mass of air passing per second is ρAv, so the available kinetic energy per second is 21(ρAv)v2=21. Doubling the wind speed gives 8 times the power, and doubling the blade length gives 4 times. No turbine can extract all of it, because the air must keep moving to leave the blades. The theoretical maximum (the Betz limit) is 59%. Real turbines lose more through blade drag, gearbox and generator losses, and by operating between a cut-in speed (about 3–4 m s⁻¹) and a cut-out speed (about 25 m s⁻¹). Above the rated speed their output is capped.
Hydroelectric and pumped storage: power =η×timemass×gh=η, where is the volume flow rate. Pumped storage stores surplus electricity as GPE and returns about 75% of it within seconds.
Tidal barrage: a basin of area A holding water to a depth h above low tide releases mg2h, because the centre of mass falls . This gives per emptying. Tides are predictable but arrive about every 12.4 hours, not on demand.
Nuclear fission and fusion
Enrichment: natural uranium is only 0.7% uranium-235. Thermal reactors need 3–5% to sustain a chain reaction, so centrifuges separate the slightly lighter U-235 (as UF₆ gas).
Breeding:238U captures a neutron to form 239U, which undergoes two β⁻ decays to fissile 239Pu. A fast breeder reactor makes more fissile fuel than it uses, which stretches uranium reserves roughly 60-fold.
Fusion (deuterium–tritium) needs about 108 K so that nuclei overcome their electrostatic repulsion, and the plasma must not touch the walls, so it is held by magnetic confinement in a tokamak. Energy gain requires the triple productnTτE (density × temperature × energy confinement time) to exceed a threshold, roughly keV s m⁻³ for D–T ignition. Questions give you the value. The fuel is abundant, and there is no long-lived fission waste and no runaway chain reaction. But the plasma is unstable, neutrons damage the reactor walls, and tritium must be bred from lithium.
Fuel cells
In a hydrogen fuel cell, hydrogen is split at the anode into H⁺ ions and electrons. The electrons flow through the external circuit (the useful current), and the ions cross the electrolyte membrane. At the cathode they combine with oxygen to form water. The only emission at the point of use is water, with no CO₂. The cell converts chemical energy directly to electrical energy, so it is not limited like a heat engine, and efficiencies reach 40–60%. The catch is that most hydrogen is still made from natural gas. The cell is only low-carbon if its hydrogen comes from electrolysis powered by renewables.
Conduction and U-values
ΔtΔQ=−AKΔxΔθ
K is the thermal conductivity (W m⁻¹ K⁻¹), and the minus sign shows that energy flows down the temperature gradient. Builders use the U-value (W m⁻² K⁻¹): rate =UAΔθ. For one layer U=ΔxK. For layers in contact (in series), the same power passes through each layer in the steady state, and the “resistances” add:
U1=K1Δx1+K2Δx2+…
The biggest temperature drop is across the layer with the largest KΔx, which is the insulation. Parallel paths, such as a wall and a window, simply add: total rate =(U1A1+U2A2)Δθ.
Worked examples
Exam technique
Show the physics behind each equation when asked to “show that”. For wind, write “mass per second =ρAv”. For tides, write “the centre of mass falls 2h”.
Scaling questions: power ∝v3 and ∝r2; the equilibrium T∝(1−a)1/4; conduction rate ∝ΔxAΔθ.
Evaluate/compare answers need both sides and a judgement: reliability (intermittent wind and solar against predictable tides), power density, cost, CO₂ per kWh, storage, and land or visual impact. For the UK: wind now supplies roughly 30% of electricity, coal generation ended in 2024 and nuclear provides about 15%. Other countries differ, for example France relies heavily on nuclear, Norway on hydro, and China and India still burn a lot of coal.
Units: keep temperatures as differences in K (a difference of 1 °C is the same as 1 K), and convert km² to m² (×106) and kWh to J (×3.6×106).
Common mistakes
Quick recap
Equilibrium: S(1−a)πR2=4πR2σT4 gives 255 K; greenhouse gases absorb the outgoing IR (about 10 µm), raising the surface to about 288 K.
The Sun is powered by the p–p chain, peaks at 500 nm and delivers about 1.36 kW m⁻² at the Earth; I=4πd2P.
Melting sea ice leaves the sea level unchanged (Archimedes); melting land ice raises it.
Wind: 21ρAv3 (Betz limit 59%). Hydro: ηρQgh. Tidal: per emptying.
Enrichment raises U-235 from 0.7% to 3–5%; breeding turns U-238 into Pu-239; fusion needs about 108 K, confinement and a large nTτE.
Fuel cells emit only water at the point of use and are not heat-engine limited, but they are only as clean as the hydrogen supply.