Energy Balance & the Greenhouse Effect
This workbook covers two physics lessons, one independent learning task, and your Collaborative Sciences Project (CSP).
- State and apply the conservation of energy to a planet's radiation balance.
- Define emissivity and use the Stefan–Boltzmann law, P = eσAT⁴.
- Explain the solar constant S, and why the mean incoming intensity on a planet is S/4.
- Define albedo, and explain why Earth's albedo varies with cloud cover and latitude.
- Explain the greenhouse effect using both the resonance model and molecular energy levels, and name the four main greenhouse gases.
- Distinguish the natural greenhouse effect from the human-caused enhanced greenhouse effect.
Part A — Lesson 1: Radiation, Emissivity, the Solar Constant and Albedo
50 minutes pairs with slides 1–19 of “The greenhouse effect and global warming”
All boards · Light
The Inverse Square
Law
Spread the same energy over a sphere and its area grows as r². So whatever you measure at a point — brightness, field strength, force — falls as 1/r². Pick a quantity, then move the detector.
Where the inverse square law turns up
Any influence that streams outward from a point and isn't absorbed obeys it — across mechanics, fields, waves and nuclear physics, and far beyond the exam spec.
?The law fails when the spreading isn't over a full sphere — a laser beam stays roughly parallel, and a long wire or charged plate spreads over a cylinder or plane, giving 1/r or a constant field instead.
A.1 Starter — conservation of energy 5 min
Energy cannot be created or destroyed; it can only be transferred from one form or place to another. This single idea, the conservation of energy, underpins everything in this unit: if a planet's average temperature is roughly constant from one year to the next, then the rate at which it absorbs energy must equal the rate at which it radiates energy away.
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A.2 Black-body radiators and the Stefan–Boltzmann law 10 min
Every object radiates electromagnetic energy because of its temperature. A black body is an idealised object that absorbs all radiation falling on it, reflecting and transmitting none. Because it doesn't reflect visible light, a cold black body looks black — but hot black bodies glow, and the hotter they are, the more power they radiate.
P = power radiated (W) A = surface area (m²) T = absolute temperature (K)
σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ (the Stefan–Boltzmann constant — it's in your data booklet)
e = emissivity of the surface (see A.3)
A tungsten filament has a surface area of 5.3 × 10⁻⁵ m², operates at 2500 K, and has emissivity 0.35. Calculate the power it radiates.
Answer:
P = eσAT⁴ = 0.35 × (5.67 × 10⁻⁸) × (5.3 × 10⁻⁵) × (2500)⁴ = 41 W
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A.3 Emissivity 8 min
e is dimensionless and 0 ≤ e ≤ 1. A perfect black body has e = 1.
Dark, dull surfaces tend to have emissivity close to 1 — they are good approximations to a black body. Shiny, silvered surfaces have emissivity close to 0: they reflect rather than absorb (and therefore emit) radiation efficiently.
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A.4 The solar constant, S, and why the mean incoming intensity is S/4 12 min
Stars radiate as black bodies. The Sun radiates a total power of about 3.85 × 10²⁶ W in all directions. By the time this radiation has spread out over a sphere the size of Earth's orbit, its intensity has dropped considerably.
For Earth: S = 1360 W m⁻² (this value is in your data booklet).
At any instant, only the side of the planet facing the Sun receives radiation — and even then, a curved surface is not everywhere perpendicular to the incoming rays. The simplest way to picture the total power intercepted is to imagine the planet's silhouette: a flat disc of radius R, with area πR², blocking the Sun's rays.
Total power intercepted by the planet: P = S × πR²
Because the planet rotates and its whole surface re-radiates that energy, the incoming power is effectively shared out over the full surface area of the sphere, 4πR², not just the disc that faces the Sun:
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A.5 Albedo 10 min
Albedo has no units and ranges from 0 (a perfectly absorbing surface) to 1 (a perfectly reflecting surface). Earth's average albedo is about 0.3.
Earth's albedo is not a fixed number. It varies from day to day and place to place, mainly because of cloud cover and latitude. Fresh cloud tops and polar ice/snow are highly reflective (locally raising the albedo); oceans and dense forest are much darker (locally lowering it). Because global cloud cover is constantly changing, and because the Sun's rays strike different latitudes at very different angles, Earth's instantaneous, whole-planet albedo drifts from day to day even though its long-term average stays close to 0.3.
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Open question. Look at Figure A.5. Towns and cities are dominated by surfaces like dark roads, roofs and car parks. Suggest two ways city planners could change the surfaces in a city to raise its local albedo, and explain the effect this could have on the local climate.
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A.6 Putting it together: the net radiation Earth absorbs 5 min
Not all of the mean incoming intensity S/4 is absorbed — a fraction α is reflected straight back to space. The net intensity absorbed is:
For Earth: (1360/4) × (1 − 0.3) = 340 × 0.7 = 238 W m⁻².
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Lesson 1 self-check
Rate yourself honestly before moving on — this is for you, not for marks. Choose a rating from the dropdown.
| Rating | I can… statement |
|---|---|
| I can state the conservation of energy and apply it to a planet's energy balance. | |
| I can define emissivity and use the Stefan–Boltzmann law, P = eσAT⁴. | |
| I can define albedo as total scattered power / total incident power. | |
| I can explain why Earth's albedo varies daily, with cloud cover and with latitude. | |
| I can state what the solar constant S represents and calculate it for another planet. | |
| I can explain why the mean incoming solar intensity on a planet is S/4, using the projected-area argument. |
Part B — Lesson 2: The Greenhouse Effect
50 minutes pairs with slides 20–23 of “The greenhouse effect and global warming”
B.1 Starter — recap 5 min
B.2 Earth's energy balance without an atmosphere 10 min
If Earth had no atmosphere, its surface would radiate as an (almost) black body directly to space. At a stable equilibrium temperature, the power absorbed equals the power emitted, so we can set the two Stefan–Boltzmann-based expressions equal to each other:
T = ⁴√[ (S/4)(1 − α) / eσ ]
Using S = 1360 W m⁻², α = 0.3 and e ≈ 1: T ≈ 255 K (about −18 °C). Earth's actual average surface temperature is about 288 K (15 °C) — roughly 33 °C warmer. That difference is due to the natural greenhouse effect.
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B.3 How greenhouse gases actually absorb and re-emit energy 15 min
Greenhouse gas molecules don't just “warm” by magic — IB Physics uses the resonance model to try to explain what is happening. A gas molecule's bonds can be modelled a little like tiny springs: the atoms can vibrate relative to one another, and each vibrational mode has its own natural frequency. When infrared radiation from Earth's surface passes through the atmosphere, it acts like a periodic driving force on these molecular “springs.” When this happens there is an effect known as resonance, which hugely increases the energy of the “springs”: a greenhouse gas molecule absorbs strongly only when the frequency of the incoming IR radiation matches (resonates with) its natural vibration frequency.
The molecular energy levels model
A more complete quantum picture treats a molecule's vibrational (and rotational) states as a set of discrete, quantised energy levels. A greenhouse gas molecule absorbs an IR photon only if the photon's energy, ΔE = hf, exactly matches the energy gap between two of its allowed vibrational energy levels. Absorbing the photon promotes the molecule to the higher (excited) level.
The molecule doesn't stay excited for long. It relaxes back towards the ground state and, in doing so, re-emits the absorbed energy as infrared radiation. Crucially, this re-emission happens in random directions — up, down, and sideways — not just back the way the original radiation came from. As you might expect, some of the re-emitted radiation heads back down towards the surface, warming it further, rather than continuing out to space.
Not every gas in the atmosphere behaves this way. Nitrogen (N₂) and oxygen (O₂) make up about 99% of the air, but neither is a greenhouse gas: they are symmetric molecules, so the way they vibrate doesn't change their charge distribution enough to couple to the oscillating electric field of IR radiation and be driven into resonance. Asymmetric molecules like CO₂ and H₂O can, which is why greenhouse gases are able to absorb IR strongly even though they're only present in trace amounts.
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B.4 The four main greenhouse gases 10 min
Water vapour, carbon dioxide, methane and nitrous oxide are the four greenhouse gases you need to know in detail. Every one of them has both natural sources and sources created by human (anthropogenic) activity.
• Evaporation from oceans, rivers and lakes • Burning fossil fuels in power stations and cars • Wetlands, oceans, lakes and rivers • Aircraft (flight) emissions • Forest fires and volcanic eruptions • Flooded rice fields, farm animals and termites • Forests, oceans, soils and grasslands • Processing of coal, natural gas and oil, and burning biomass • Manufacture of cement and fertilisers, and deforestation
| Greenhouse gas | Formula | Natural sources | Anthropogenic sources |
|---|---|---|---|
| Water vapour | H₂O (g) | ||
| Carbon dioxide | CO₂ | ||
| Methane | CH₄ | ||
| Nitrous oxide | N₂O |
| Greenhouse gas | Formula | Natural sources | Anthropogenic sources |
|---|---|---|---|
| Water vapour | H₂O (g) | Evaporation from oceans, rivers and lakes | Flight (aviation emissions) |
| Carbon dioxide | CO₂ | Forest fires, volcanic eruptions, evaporation/outgassing from oceans | Burning fossil fuels in power plants and cars, burning forests |
| Methane | CH₄ | Wetlands, oceans, lakes and rivers | Flooded rice fields, farm animals, termites, processing of coal/natural gas/oil, burning biomass |
| Nitrous oxide | N₂O | Forests, oceans, soils and grasslands | Burning fossil fuels, manufacture of cement and fertilisers, deforestation |
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B.5 The enhanced greenhouse effect 5 min
The natural greenhouse effect keeps Earth roughly 33 °C warmer than it would otherwise be — without it, Earth would likely be too cold to support life as we know it. The enhanced greenhouse effect refers specifically to the additional warming caused by human activity increasing the atmospheric concentration of greenhouse gases beyond their natural levels.
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Lesson 2 self-check
Rate yourself honestly before moving on — this is for you, not for marks. Choose a rating from the dropdown.
| Rating | I can… statement |
|---|---|
| I can calculate a planet's no-atmosphere equilibrium temperature from S, albedo and emissivity. | |
| I can explain the greenhouse effect using the resonance model, including re-emission in all directions. | |
| I can explain why N₂ and O₂ are not greenhouse gases, but CO₂ and H₂O are. | |
| I can name the four main greenhouse gases and at least one natural and one anthropogenic source for each. | |
| I can distinguish the natural greenhouse effect from the enhanced (human-caused) greenhouse effect. |
Part C — Synthesis Task: Reading Real Planetary Energy Budgets
Sylvia Knight's “Planetary energy budgets” infographic (Physics Review, February 2016) shows measured energy-flow data for Mars, Venus, Titan and Jupiter, each drawn the same way as the Earth energy-balance diagram on slide 20. Ask your teacher to display it so you can work through the questions below — the key numbers for Venus are reproduced in the table so you can calculate with them directly.
| Venus energy budget (selected values) | Intensity / W m⁻² |
|---|---|
| Incoming solar radiation (short-wave) | 656 |
| Total short-wave reflected to space | 496 |
| Net energy absorbed by surface | 22 |
| Long-wave infrared radiation emitted to space | 161 |
| Long-wave infrared radiation emitted by surface, absorbed by atmosphere | 17 154 |
| Long-wave infrared radiation emitted by atmosphere back down to surface | 17 132 |
| Net energy emitted by surface | 22 |
(Data adapted from Knight, S., “Planetary energy budgets,” Physics Review, February 2016, Hodder Education.)
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Part D — Your Collaborative Sciences Project
The Collaborative Sciences Project (CSP) gives you the chance to work in an interdisciplinary team on a real scientific question, using the physics of energy balance and the greenhouse effect you've just met — but seen through the lens of a genuine investigation rather than a textbook problem. The purpose of the CSP is for students to collaborate to identify a problem using science-based reasoning, leading to action. The focus is on the process of collaborative problem-solving, not on producing a single “correct” product, and the CSP itself is not formally assessed.
Sample outcomes for your project
Your outcome shouldn't be a physics experiment alone — data is used to inform actions. What action would you plan or suggest? Almost any local action can work, provided it's grounded in the physics of energy balance and clearly linked to either changing the albedo of the area, reducing carbon dioxide emissions, or the tree/shrub coverage of the area.
- A local rubbish-picking or clean-up drive that also promotes walking dogs locally instead of driving, cutting local vehicle emissions.
- A fashion show promoting second-hand clothing, to reduce the energy cost of producing new clothes.
- A publicity campaign encouraging people to delete unused files from cloud storage, to reduce the energy used by data centres.
- Designing simple sensors that help reduce a building's energy use.
- Modelling and proposing the most effective recycling system for your school.
- A campaign for reflective, brightly-coloured roofs and “white roads” (light-coloured road surfacing), to raise the local albedo.
- A campaign promoting more solar panels on roofs.
The product could be a scientific poster, a planning document, or something to inspire action such as visual art (e.g. painting, sculpture, installation), performing art (e.g. theatre, film, music, dance), or literature (e.g. poetry, short story). Whatever the medium, it must connect to both a local context and a global issue, be documented in a process journal (in a medium of your choice — video, narrated presentation, booklet, website), and be shared with the school community.
D.1 Project proposal (complete in Session 1, then get mentor sign-off)
Risk assessment
| Hazard | Who might be harmed? | Control measures |
|---|---|---|
D.2 Sample experiments
These two options are illustrative starting points for your investigation — your own project doesn't have to be exactly either one, provided it's grounded in the same physics.
Option A — Measuring the albedo of different surfaces
Links directly to Understandings: albedo formula; Earth's albedo varies with cloud/latitude; conservation of energy
Aim. To measure and compare the albedo of a range of real surfaces (e.g. grass, tarmac/concrete, bare soil, white card, aluminium foil, water, gravel), and relate your results to why Earth's own albedo varies with cloud cover, ice cover and latitude.
Background theory. Albedo α = total scattered power ÷ total incident power. A real satellite-based albedometer uses a matched pair of sensors — one facing the sky to record incoming (incident) intensity, one facing the ground to record reflected intensity — and takes the ratio. You will build a simplified version of the same method.
Analysis & evaluation prompts:
- Rank your surfaces from lowest to highest albedo. Does the order match what you'd predict from colour/texture?
- How would your results change on a cloudy day compared with a clear day? Link your answer to why Earth's whole-planet albedo varies daily.
- What is the main source of uncertainty in your method? How could a real satellite-based measurement avoid it?
- If your school is at a high or low latitude, discuss how the angle of the Sun's rays might affect your measured values at different times of day.
Option B — Energy transfer under different foliage/canopy coverings
Links directly to Understandings: solar constant S and S/4; conservation of energy; absorption/emission of radiation
Aim. To investigate how different types or densities of foliage/canopy covering affect the amount of solar energy reaching the ground beneath them, as a simple physical model for how vegetation cover and land use affect a local (and, in aggregate, global) energy budget.
Background theory. A canopy of leaves — or an artificial substitute such as shade netting of different grades — intercepts and scatters incoming short-wave solar radiation before it reaches the ground, in much the same way that clouds intercept sunlight over the oceans (A.5). Comparing the energy reaching the ground with and without different coverings lets you quantify a “local albedo/shielding effect.” Note: this experiment models shielding of incoming shortwave radiation, which is not the same mechanism as the atmospheric greenhouse effect (which traps outgoing longwave radiation) — a good discussion point for your evaluation.
Analysis & evaluation prompts:
- Which covering blocked the most energy? Does this match the density/thickness you observed?
- Estimate, using your control reading and S = 1360 W m⁻², what fraction of the actual solar constant your open-sky reading represents (accounting for cloud cover, angle of the Sun, and atmospheric losses).
- Explain, in your own words, why this experiment models shielding of incoming shortwave radiation rather than the trapping of outgoing longwave radiation that defines the atmospheric greenhouse effect.
- What real-world land-use decision could your data inform (e.g. urban tree planting, greenhouse/polytunnel design, solar panel siting)?
D.3 Sharing the outcome of your project
Your data informed something — but what? What will you now do? That outcome or action needs to be shared alongside your scientific data, not treated as an afterthought. Choose whichever medium suits your team, your data and your action best: a scientific poster, a short video, a podcast, a slide deck, a web page, or another format agreed with your mentor. Whatever the format, make sure it includes:
- The investigation question and its link to a local context and a global issue.
- Your method, in enough detail that someone else could repeat it.
- Your data and at least one clear graph or table.
- Your conclusion and evaluation, and how they informed the action you took (or plan to take).
- A description of the action itself — what you did, planned or executed, and why.
D.4 Individual 100-word reflection
Write this individually, honestly, and specifically — it should be a genuine commentary on your experience, not a list of what you did. Consider:
- A challenge and a success in collaborating with your team.
- A challenge and a success in communicating your ideas or findings.
- One thing you now understand about energy balance or the greenhouse effect that you didn't before.
- One or two salient successes, and one or two challenges and how your team overcame them.
- A brief reflection on how your approach to learning skills — particularly collaboration and communication — developed over the project.
Part E — Understanding Coverage Checklist
For teacher (and student) reference: exactly where each required Understanding is introduced, practised and evidenced.
| # | Understanding | Introduced in | Workbook Qs | Further evidence | ✓ |
|---|---|---|---|---|---|
| 1 | The conservation of energy. | A.1 (starter); B.2 (energy-balance derivation) | Q1, Q1b, Q13 | CSP data analysis — checking absorbed ≈ emitted | |
| 2 | Emissivity as the ratio of the power radiated per unit area by a surface compared to that of an ideal black surface at the same temperature. | A.2–A.3 | Q2, Q3 | Lesson 1 self-check | |
| 3 | Albedo as a measure of the average energy reflected off a macroscopic system: albedo = total scattered power / total incident power. | A.5, Figures A.4–A.5 | Q5, Q12 | CSP Option A directly measures albedo | |
| 4 | Earth's albedo varies daily and is dependent on cloud formations and latitude. | A.5 | Q5, Q5b (open, city albedo) | CSP Option A (weather-condition notes); Lesson 1 self-check | |
| 5 | The solar constant, S. | A.4 | Q4 | CSP Option B (comparison to S) | |
| 6 | Incoming radiative power depends on the planet's projected surface along the direction of the rays, giving a mean incoming intensity of S/4. | A.4 (with Figure A.1 diagram) | Q4, Q6 | Synthesis Part C | |
| 7 | Methane, water vapour, carbon dioxide and nitrous oxide are the main greenhouse gases, each with both natural and human (anthropogenic) origins. | B.4 | Q10 & sorting table | Lesson 2 self-check | |
| 8 | Absorption of infrared radiation by the main greenhouse gases in terms of molecular energy levels, and subsequent emission of radiation in all directions. | B.3 (The molecular energy levels model), Figure B.2 | Q9 | Part C, Q14 (Venus) | |
| 9 | The greenhouse effect can be explained in terms of both a resonance model and molecular energy levels. | B.3, Figures B.1–B.2 | Q9 | — | |
| 10 | The augmentation of the greenhouse effect due to human activities is known as the enhanced greenhouse effect. | B.5 | Q11 | CSP reflection (D.4) |