This mini-lesson covers Eduqas Component 3, Option D: the Earth's thermal equilibrium and the effect of CO₂; Wien's law and Stefan's law in a solar context; Archimedes and sea level rise; solar, wind, tidal, hydroelectric and pumped storage power; nuclear fission and fusion; fuel cells; and thermal conduction and U-values.
⚠️ This is an OPTION. Eduqas Component 3 Section B offers four options — A Alternating Currents, B Medical Physics, C The Physics of Sports, D Energy and the Environment. You study exactly ONE of them. Only work through this mini-lesson if Option D: Energy and the Environment is the one your school teaches. Everyone also needs the Component 3 core (Sections 1–10), which has its own mini-lesson.
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The Earth is in thermal equilibrium when the power it absorbs from the Sun equals the power it re-radiates to space. If the outgoing power falls below the incoming power, the Earth warms until balance is restored at a higher temperature.
The Sun is very hot (~5800 K), so by Wien's law its radiation peaks in the visible — which passes freely through the atmosphere. The Earth is far cooler (~288 K), so its radiation peaks in the infrared. Greenhouse gases — CO₂, water vapour, methane — are largely transparent to visible light but strongly absorb infrared. Radiation gets in easily and out with difficulty, so the surface settles at a higher temperature. Rising CO₂ levels tighten that infrared "blanket".
Archimedes and sea level (a)(iv): a floating iceberg already displaces its own weight of water — so when it melts, the meltwater exactly fills the volume it was displacing and the sea level does not change. Ice sitting on land (Greenland, Antarctica) is displacing nothing; when it melts it adds entirely new water to the ocean and the sea level rises. (Thermal expansion of the warming water raises it further.)
The Sun's energy comes from the proton–proton chain: hydrogen nuclei fuse, ultimately forming helium-4, and the small loss of mass appears as energy (E = mc²).
Photovoltaic cells convert solar radiation directly into electrical energy, typically at 15–25% efficiency. Useful electrical power = intensity × panel area × efficiency.
Where the cube comes from: the kinetic energy of the fluid is ½mv², and the mass arriving per second is ρAv — so the power is ½(ρAv)v² = ½ρAv³. Doubling the wind speed gives eight times the power, which is why turbine siting matters so enormously.
Efficiency limits: a turbine can never take all the kinetic energy — the air must keep moving to get out of the way (the theoretical maximum, the Betz limit, is about 59%; real turbines manage roughly 40%). Other factors: blade design, drag and generator losses, and the fact that turbines must shut down in very high winds.
Tidal barrages, hydroelectric and pumped storage all work by the same conversion: gravitational potential energy → kinetic energy → electrical energy.
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Fission — enrichment and breeding. Natural uranium is over 99% U-238, which does not readily fission with slow neutrons; only about 0.7% is the fissile U-235. Enrichment raises the U-235 fraction to a few percent to sustain a chain reaction. Breeding converts otherwise useless U-238 into fissile plutonium-239 by neutron capture — turning the bulk of the uranium into fuel, at the cost of producing weapons-usable material.
Fusion — why it is so hard. Two positive nuclei must be pushed close enough for the strong nuclear force to grip, against enormous Coulomb repulsion. That means temperatures over 10⁸ K — at which the fuel is a plasma that no material container can touch, so it must be confined magnetically (a tokamak) or inertially (laser compression). Success requires the triple product — the product of the plasma density, its temperature and the confinement time — to exceed a threshold value. Achieving any one of the three is easy; achieving all three at once is the entire problem.
Fuel cells combine hydrogen and oxygen electrochemically to produce electricity directly, with water as the only product at the point of use — no CO₂, no particulates, and higher efficiency than a heat engine (which is limited by thermodynamics). The catch: the hydrogen has to be made, and if it is made by reforming natural gas, the CO₂ has simply been moved rather than removed. Green hydrogen (electrolysis powered by renewables) fixes that, at a cost.
To cut the heat loss you can reduce K (a better insulator), reduce A, or increase the thickness Δx. A trapped layer of air is an excellent insulator (very low K) — which is exactly what cavity wall insulation, double glazing and a wool jumper all exploit.
Materials in contact: for layers in series, the same power flows through each layer, and the temperature drop across each is proportional to its thermal resistance. The U-value of the composite is found from 1/U = sum of (Δx/K) for each layer, plus the surface resistances.
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Energy balance: in = out at equilibrium; Sun peaks visible, Earth peaks infrared; CO₂ absorbs the infrared
Sea level: floating ice → no change (Archimedes); land ice → rise (plus thermal expansion)
Solar: proton–proton chain; I = P/4πd²; PV output = I × A × efficiency
Wind: P = ½ρAv³ — power goes as v³, so doubling the wind gives 8× the power
Water: tidal, hydro and pumped storage all convert E(p) → E(k) → electrical; pumped storage is a store, not a source
Nuclear: enrichment and breeding (fission); the fusion triple product — density × temperature × confinement time
Fuel cells: water is the only product at the point of use — but the hydrogen has to be made
Insulation: Q/t = KAΔθ/Δx; rate = UAΔθ; low U-value = good insulator
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You have worked through Option D: Energy and the Environment for Eduqas A-level Physics. 🎉
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