P25: Black Body Radiation
Black body radiation and temperature
📋 Key Definitions
Black body: An object that absorbs all the electromagnetic radiation incident on it. No radiation is reflected or transmitted. A black body is also the best possible emitter of radiation — it emits radiation at the maximum possible rate for any object at that temperature.
Perfect black body: An idealised object that absorbs and emits all possible radiation. No real object is a perfect black body, but a small hole in a cavity is a very close approximation.
Black body radiation: The electromagnetic radiation emitted by a black body. The distribution of wavelengths depends only on the object's temperature.
📝 How Temperature Affects Radiation
Key principles:
1. As temperature increases, a black body emits radiation at a greater rate (more radiation per second).
2. As temperature increases, the peak wavelength of the emitted radiation becomes shorter (shifts towards the blue/violet end of the spectrum).
1. As temperature increases, a black body emits radiation at a greater rate (more radiation per second).
2. As temperature increases, the peak wavelength of the emitted radiation becomes shorter (shifts towards the blue/violet end of the spectrum).
Temperature and Peak Wavelength
All objects emit electromagnetic radiation across a range of wavelengths. The intensity of radiation varies with wavelength, producing a curve on a graph. The peak of this curve shows the wavelength emitted with the greatest intensity.
| Temperature | Total radiation emitted | Peak wavelength | Appearance |
|---|---|---|---|
| Low (e.g. 3000 K) | Less | Longer (infrared) | Glowing red |
| Medium (e.g. 5500 K) | More | Medium (visible light) | White/yellow |
| High (e.g. 10000 K) | Much more | Shorter (blue/UV) | Blue-white |
Why hotter objects appear different colours: A cooler star (like Betelgeuse, ~3500 K) emits most intensely in the infrared and lower visible range, so it appears red. A hotter star (like Rigel, ~12000 K) peaks in the blue/UV range, so it appears blue-white. Our Sun (~5800 K) peaks in the green-yellow part of the visible spectrum.
🌍 Earth's Temperature and Radiation
Energy balance: The temperature of the Earth depends on the balance between the radiation it receives from the Sun and the radiation it emits back into space. If the Earth absorbs more radiation than it emits, it warms up. If it emits more than it absorbs, it cools down.
Factors Affecting Earth's Temperature
- Solar radiation: The Sun emits radiation (mostly visible light and infrared). Some is absorbed by the Earth, some is reflected back by clouds and the atmosphere.
- Earth's emitted radiation: The Earth, being much cooler than the Sun, emits infrared radiation back into space.
- Greenhouse gases: Gases like carbon dioxide, methane and water vapour in the atmosphere absorb some of the infrared radiation emitted by the Earth and re-emit it in all directions — including back towards the surface. This traps heat and warms the Earth.
Increased greenhouse effect: If the concentration of greenhouse gases increases, more infrared radiation is absorbed and re-emitted back towards Earth. Less radiation escapes into space. This means the Earth absorbs more radiation than it emits, so its temperature rises until a new, higher equilibrium is reached.
| Factor | Effect on Earth's temperature | Mechanism |
|---|---|---|
| Increased greenhouse gases | Temperature rises | More IR absorbed and re-emitted towards Earth; less radiation escapes to space |
| Increased solar radiation | Temperature rises | More radiation absorbed by Earth |
| Increased albedo (reflection) | Temperature falls | More radiation reflected away before being absorbed |
| Decreased greenhouse gases | Temperature falls | Less IR trapped; more radiation escapes to space |
🧮 Worked Examples
Example 1: Comparing stars
Star A has a surface temperature of 3000 K. Star B has a surface temperature of 12000 K. Compare the radiation emitted by the two stars.
Solution:
Star B is hotter, so it emits more radiation per unit area per second than Star A. Star B's peak wavelength is shorter (more towards blue/UV) than Star A's peak wavelength (more towards infrared/red). Star B would appear blue-white while Star A would appear red.
Example 2: Earth's energy balance
Explain why the Earth's temperature would increase if the amount of carbon dioxide in the atmosphere doubled.
Solution:
Carbon dioxide is a greenhouse gas. It absorbs infrared radiation emitted by the Earth and re-emits it in all directions, including back towards the surface. If CO2 doubles, more infrared radiation is absorbed and re-emitted towards Earth. This means less radiation escapes to space. The Earth now absorbs more radiation than it emits, so its temperature rises until a new equilibrium is reached at a higher temperature.
Example 3: Temperature and peak wavelength
A black body at 4000 K emits radiation with a peak wavelength in the red part of the visible spectrum. If the temperature increases to 8000 K, what happens to the peak wavelength and the total radiation emitted?
Solution:
When the temperature doubles from 4000 K to 8000 K: (1) The peak wavelength becomes shorter — it shifts from red towards the blue/violet end of the spectrum. (2) The total radiation emitted increases significantly (it is proportional to T to the power 4, so it increases by a factor of 2 to the power 4 = 16 times). The object emits much more radiation at a shorter peak wavelength.
❓ Practice Questions
Q1: Higher Define what is meant by a black body.
Q2: Higher Describe two ways that increasing the temperature of a black body affects the radiation it emits.
Q3: Higher Explain how increasing the concentration of greenhouse gases in the atmosphere causes global warming.
Q4: Higher A red giant star and a white dwarf star are observed. The white dwarf has a much higher surface temperature. Compare the total radiation emitted per second and the peak wavelength of the two stars.
Q5: Higher Explain why the Earth's temperature remains roughly constant under normal conditions.
✅ Answers
- Q1: A black body is an object that absorbs all the electromagnetic radiation incident on it. It does not reflect or transmit any radiation. It is also the best possible emitter of radiation at any given temperature.
- Q2: (1) The total rate of radiation emitted increases — a hotter body emits more radiation per second. (2) The peak wavelength of the emitted radiation becomes shorter — it shifts towards the higher-frequency (blue/violet) end of the spectrum.
- Q3: Greenhouse gases (such as CO2 and methane) absorb infrared radiation emitted by the Earth's surface and re-emit it in all directions, including back towards the surface. This means less radiation escapes to space. If greenhouse gas concentration increases, more IR is trapped, the Earth absorbs more than it emits, and the temperature rises until a new equilibrium at a higher temperature is reached.
- Q4: The white dwarf has a higher surface temperature so it emits more radiation per unit area per second than the red giant. The white dwarf's peak wavelength is shorter (in the blue/white region) while the red giant's peak wavelength is longer (in the red/infrared region). The red giant may emit more total radiation because it has a much larger surface area, even though the intensity per unit area is less.
- Q5: Under normal conditions, the Earth is in thermal equilibrium — the average amount of radiation absorbed from the Sun equals the average amount of radiation emitted back into space. Any change in temperature is corrected by the balance: if the Earth warms slightly, it emits more radiation; if it cools, it emits less. This keeps the temperature roughly constant.
🎯 Exam Tips
- This topic is Higher Tier only — it will not appear on Foundation papers.
- Always state BOTH effects of temperature increase: more radiation emitted AND shorter peak wavelength.
- For Earth's temperature questions, always discuss the balance between radiation absorbed and radiation emitted. Use the word "equilibrium".
- When explaining the greenhouse effect, be precise: greenhouse gases absorb infrared radiation (not UV, not visible light) emitted by the Earth.
- Don't confuse "black body" with "black hole" — a black body emits radiation; it just absorbs all incident radiation.
- The Sun is not a perfect black body, but it is a good approximation for GCSE questions.
🔢 Maths Skills
Mathematical Skills
Interpreting black body radiation curves: the x-axis shows wavelength, the y-axis shows intensity. Higher temperature curves are taller (more total radiation) and peak at shorter wavelengths. The total power radiated is proportional to T⁴ (Stefan-Boltzmann law), so doubling the temperature increases power by 2⁴ = 16 times. Reading values from graphs and comparing areas under curves.
Maths Example
Star X has a surface temperature of 4000 K and radiates power at a rate of P. Star Y has a surface temperature of 8000 K and the same surface area. How many times more power does Star Y radiate? Ratio = (8000/4000)⁴ = 2⁴ = 16. Star Y radiates 16 times more power per unit area than Star X.
⚠️ Common Misconceptions
Watch Out!
1. Wrong: A black body is black in colour and therefore does not emit radiation Correct: A black body absorbs all radiation incident on it but is also the best possible emitter — at high temperatures it can glow any colour from red to blue-white
2. Wrong: Hotter objects emit more radiation because they have a longer peak wavelength Correct: Hotter objects emit MORE radiation overall but at a SHORTER peak wavelength — the peak shifts towards blue/violet as temperature increases
3. Wrong: Greenhouse gases trap visible light from the Sun Correct: Greenhouse gases absorb infrared radiation emitted by the Earth — they are largely transparent to visible light from the Sun which passes through and warms the surface
✍️ 6-Mark Question
Extended Answer
6 marks: Explain how the balance between radiation absorbed and radiation emitted determines the Earth's temperature. Discuss how human activities could affect this balance.
The Earth's temperature depends on the balance between incoming solar radiation (mostly visible light and infrared) and outgoing radiation emitted by the Earth (infrared). When the Earth absorbs the same amount of radiation as it emits, the temperature stays roughly constant (thermal equilibrium). The Earth absorbs visible light from the Sun and warms up. It then emits infrared radiation back into space. Greenhouse gases in the atmosphere (CO₂, methane, water vapour) absorb some of this outgoing infrared radiation and re-emit it in all directions, including back towards the surface. This traps heat and keeps the Earth warmer than it would be otherwise. Human activities such as burning fossil fuels, deforestation and agriculture increase the concentration of greenhouse gases in the atmosphere. More greenhouse gases means more infrared radiation is absorbed and re-emitted towards Earth, so less escapes to space. The Earth now absorbs more radiation than it emits, causing the temperature to rise until a new equilibrium is reached at a higher temperature — this is global warming.
Mark scheme: 1 mark — temperature depends on balance of absorbed vs emitted radiation, 1 mark — equilibrium when absorbed = emitted, 1 mark — Earth absorbs visible light and emits infrared, 1 mark — greenhouse gases absorb and re-emit IR towards Earth, 1 mark — human activities increase greenhouse gas concentration, 1 mark — more greenhouse gases means less IR escapes so temperature rises
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
Data from two stars is recorded: Star A has surface temperature 3500 K and peak wavelength 830 nm. Star B has surface temperature 10,000 K and peak wavelength 290 nm. A scientist measures a new star, Star C, with a peak wavelength of 500 nm.
(a) Estimate the surface temperature of Star C, explaining your reasoning using the pattern in the data.
(b) Star A has a much larger surface area than Star B. Despite this, explain why Star B could still emit more total power per unit area.
(c) A student claims "Star A must be very dim because it has the longest peak wavelength." Evaluate this claim.
Answers: (a) As temperature increases, peak wavelength decreases. The product of temperature and peak wavelength is roughly constant: 3500 × 830 ≈ 2,905,000 and 10,000 × 290 = 2,900,000. For Star C: T ≈ 2,900,000 ÷ 500 ≈ 5800 K (similar to the Sun). (b) Total power per unit area is proportional to T⁴. Star B at 10,000 K radiates (10,000/3,500)⁴ ≈ 66.6 times more power per unit area than Star A. Star B's higher temperature far outweighs Star A's larger surface area for power per unit area. (c) The claim is misleading. Star A has a lower surface temperature so it emits less radiation per unit area and its peak is in the infrared (so less visible light), but it could still appear bright if it has a very large surface area. Total luminosity depends on both temperature AND surface area.
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🎬 Video Resources
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