IB Physics HLClimate & the Greenhouse EffectPaper 1 & 2Solar Radiation~11 min read
Albedo & Emissivity
Sunlight arrives at a planet — but what happens next? Some bounces straight back to space, and some is soaked up and later re-radiated as heat. Two numbers capture this: albedo measures how much radiation a surface reflects, and emissivity measures how well it radiates compared to a perfect black body. Together they decide how warm a planet gets, and they’re the building blocks of every energy-balance model.
📘 What you need to know
Emissivitye = the ratio of power radiated per unit area by a surface to that of a black body at the same temperature
A perfect black body has emissivity e = 1; real objects have e < 1
The Stefan-Boltzmann law for a non-black body becomes P = eσAT4
Albedoa = the ratio of total scattered (reflected) power to total incident power
Albedo has no units — it’s a ratio; an albedo of 1 reflects everything
Earth’s average albedo is about 0.30 (30% of sunlight is reflected)
Albedo varies with cloud cover, season, latitude, terrain and the angle of incidence
Emissivity
Stars behave almost exactly like black bodies — perfect emitters of radiation. Planets don’t; they radiate less than an ideal black body would at the same temperature. We measure that shortfall with emissivity.
Emissivity — definition
The ratio of the power radiated per unit area by a surface to that radiated by a black body at the same temperature
As an equation, that’s simply:
Emissivitye = (power radiated by the object) ÷ (power radiated by a black body)
The comparison assumes the black body is at the same temperature and has the same dimensions as the object. For a perfect black body the two powers are equal, so e = 1; every real surface falls somewhere below that.
At the same temperature, a black body (e = 1) radiates the most possible. A real surface radiates less, so its emissivity is below 1. Emissivity is the ratio of the two.
When we apply the Stefan-Boltzmann law to a surface that isn’t a perfect black body, we simply multiply by its emissivity:
Stefan-Boltzmann law (non-black body)P = eσAT4
Here P is the total power radiated (W), e is the emissivity, σ is the Stefan-Boltzmann constant (5.67 × 10−8 W m−2 K−4), A is the surface area (m2), and T is the absolute temperature (K). Setting e = 1 recovers the black-body version.
Worth memorising: a perfect black body has emissivity exactly 1, and that fact is not in the data booklet — examiners expect you to just know it. It’s the anchor for every emissivity question: you’re always comparing a real surface against that ideal “e = 1” benchmark.
WE 1
A surface radiates 320 W. A black body of the same size and temperature would radiate 500 W. Find the emissivity of the surface.
Step 1 — use the emissivity ratio
e = (power radiated by object) ÷ (power by black body)
Step 2 — substitutee = 320 ÷ 500e = 0.64No units — it’s a pure ratio. Below 1, as every real surface must be.
WE 2
A surface of area 2.0 m2 and emissivity 0.85 sits at a temperature of 300 K. Calculate the total power it radiates. (σ = 5.67 × 10−8 W m−2 K−4.)
Step 1 — use P = eσAT⁴P = 0.85 × (5.67×10⁻⁸) × 2.0 × (300)⁴Step 2 — evaluate (300⁴ = 8.1×10⁹)P = 0.85 × 5.67×10⁻⁸ × 2.0 × 8.1×10⁹P = 780 WThe emissivity scales down what a black body of the same area and temperature would emit.
Albedo
Emissivity is about radiation leaving a surface. Albedo is about radiation bouncing off it. It measures the fraction of incoming radiation that a surface scatters straight back.
Albedo — definition
The ratio of the total scattered (reflected) power to the total incident power of radiation at a surface
For a whole planet, albedo is the ratio of all the radiation it reflects to all the radiation that hits it. Since it’s a ratio of two powers, albedo has no units — it just runs from 0 (absorbs everything) to 1 (reflects everything). Earth’s average albedo is taken as about 0.30, meaning roughly 30% of the Sun’s rays reaching us are scattered back out.
Dark surfaces like asphalt reflect almost nothing (low albedo); bright surfaces like fresh snow reflect most of the light (high albedo). Earth’s mix averages around 0.30.
A planet’s albedo isn’t fixed — on Earth it changes day to day. The main influences are the cloud cover and season (thicker cloud reflects more), the latitude, the terrain (different materials reflect differently), and the angle at which the radiation strikes. It helps to know some typical values:
Surface
Typical albedo
Fresh asphalt
0.04
Bare soil
0.17
Green grass
0.25
Desert sand
0.40
New concrete
0.55
Ocean ice
0.50 – 0.70
Fresh snow
0.85
WE 3
The average albedo of fresh snow is 0.85. Calculate the ratio of the energy absorbed by fresh snow to the energy it reflects.
Step 1 — albedo is the reflected fraction
reflected = 0.85 of the incident energy
Step 2 — the rest is absorbed
absorbed = 1 − 0.85 = 0.15
Step 3 — take the ratioabsorbed ÷ reflected = 0.15 ÷ 0.85= 0.18Snow reflects far more than it absorbs — which is exactly why melting snow (lower albedo) speeds up warming.
WE 4
A planet receives 800 W of incident solar power on a region and scatters 240 W of it back to space. Find the albedo of that region, and state the fraction absorbed.
Step 1 — albedo = scattered ÷ incidenta = 240 ÷ 800a = 0.30Step 2 — absorbed fraction
absorbed = 1 − 0.30 = 0.70
An albedo of 0.30 is Earth’s average — 30% reflected, 70% absorbed to warm the surface.
Incident radiation 100%
albedo a
Reflected a
rest = 1 − a
Absorbed 1 − a
🛠️ Tackling albedo & emissivity questions
Emissivity = radiated power ÷ black-body power (same T and size). Black body = 1.
Radiated power? Use P = eσAT4 — don’t forget the e.
Albedo = reflected power ÷ incident power. It’s a fraction with no units.
Absorbed fraction = 1 − albedo.
Watch the temperature — always in kelvin, and raised to the fourth power.
💡 Top tips
Black body e = 1 — memorise it; it’s not in the data booklet.
Absorbed = 1 − albedo. The two fractions always add to 1.
Both are unitless ratios — if you get units, something’s wrong.
Temperature in kelvin, and to the fourth power in Stefan-Boltzmann.
Quick recap: Emissivity e compares a surface’s radiated power to a black body’s (e = 1 for a black body), giving P = eσAT4. Albedo a is the reflected fraction of incident radiation, so the absorbed fraction is 1 − a. Both are unitless, and Earth’s albedo is about 0.30.
⚠ Common mistakes
Forgetting the emissivity e in the Stefan-Boltzmann law P = eσAT4
Giving albedo or emissivity units — both are pure ratios
Using temperature in °C instead of kelvin, or forgetting the fourth power
Mixing up albedo (reflected) with the absorbed fraction (1 − albedo)
Assuming a real object has e = 1 — only a perfect black body does
You’ve now got both halves of a planet’s radiation story: albedo for what bounces off, emissivity for what’s radiated away. Put them together with the incoming solar power and you can balance a planet’s entire energy budget — which is exactly where we’re heading. Next we look at the greenhouse gases that intercept the outgoing infrared, before assembling the full energy-balance model.
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