Black Body Radiation

Every object with a temperature above absolute zero (-273 °C) emits infrared radiation. You feel it as heat from a radiator across the room, from the sun on your face, or from a mug of tea on your palm.

Key idea 1 — the hotter the object, the more IR it emits per second. A glowing fire emits enormous amounts of IR (and some visible light). A cold radiator emits very little. The rate of IR emission rises steeply with temperature.

Key idea 2 — thermal equilibrium. An object in steady state absorbs IR from its surroundings at the same rate as it emits IR. If you stand in a 20 °C room you absorb IR from the walls and emit IR back; the two rates are equal, so your skin temperature stays constant.

• If an object is hotter than its surroundings, it emits more IR than it absorbs → it cools.
• If an object is cooler than its surroundings, it absorbs more IR than it emits → it warms.
• This is why a kettle off the heat slowly cools to room temperature, and a chilled drink slowly warms.

Key idea 3 — surface matters, not the inside. Whether a surface emits IR well or badly depends on its colour and texture, not the material underneath. A copper block painted matt black emits IR like a black surface; a wooden block covered in shiny aluminium foil emits like a foil surface. AQA examiners stress this — it's the surface you observe.

Two surface properties matter: colour (dark vs light) and texture (matt vs shiny).

Best emitters AND absorbers.

• Matt black surfaces. Examples: the inside of a kettle, the heating element of a toaster, the back of a fridge.

Worst emitters AND absorbers (best reflectors).

• Shiny silver, shiny white. Examples: aluminium foil, an emergency 'space blanket', a polished teapot.

The same surface plays both roles. A surface that is good at emitting IR is also good at absorbing IR. This is a fundamental property — formalised in physics by Kirchhoff's law (not on the AQA spec, but explains why the rule works).

Comparison table.

Surface	Emission	Absorption	Reflection
Matt black	Best	Best	Worst
Matt white	Poor	Poor	Better
Shiny silver / white	Worst	Worst	Best

Real-world applications.

• Solar water heaters on UK rooftops have matt-black absorber plates — to absorb as much sunlight (visible + IR) as possible.
• Emergency 'space blankets' are shiny silver to reflect body IR back to the casualty and stop them losing heat — and to be visible to rescuers.
• Marathon runners sometimes wrap themselves in foil at the finish line for the same reason — minimise heat loss to the cool air.
• Teapots are traditionally polished silver or shiny ceramic — bad emitters of IR, so the tea stays hot.
• Fridge backs are painted matt black — best emitters of IR, so the heat extracted from inside is radiated efficiently to the kitchen.
• Houses in hot countries are often painted white to reflect sunlight (visible + IR) and stay cool.

The classic UK school investigation is the Leslie cube experiment (named after John Leslie, 1804). It demonstrates very neatly that surface colour and texture decide how much IR is emitted.

Apparatus.

• A hollow metal cube (≈ 10 cm sides). The four vertical faces have different surfaces:
  • Matt black
  • Matt white
  • Shiny black (polished)
  • Shiny silver / aluminium
• An infrared detector (thermopile + voltmeter, or an electronic IR sensor).
• Boiling water (poured carefully into the cube) — provides a uniform internal temperature.
• A thermometer or temperature probe to confirm the cube is at a steady temperature.

Procedure.

1. Fill the cube with boiling water and put the lid on. Wait until the cube has reached steady temperature (each face the same).
2. Place the IR detector at a fixed distance (e.g. 10 cm) from the matt-black face. Record the reading.
3. Without changing the distance, rotate the cube to present each of the other three faces in turn and record the IR reading from each.
4. Compare the readings.

Typical results.

Surface	Detector reading (relative)
Matt black	Highest (≈ 1.00)
Matt white	Lower (≈ 0.70)
Shiny black	Lower again (≈ 0.50)
Shiny silver	Lowest (≈ 0.20)

Conclusion. All four faces are at the same temperature, so any difference in IR emission is due to the surface alone. Matt-black surfaces emit IR best; shiny silver worst.

Why control the distance. IR intensity follows an inverse-square law with distance. Moving the detector 1 cm closer to the matt-black face would give a much higher reading and invalidate the comparison. Fix the geometry, change only the face.

Leslie cube (hollow, filled with boiling water)

IR sensor

All faces at same T → differences are due to SURFACE alone.

Controlling for fairness.

• Same cube (same temperature on each face) — the water keeps the inside uniform.
• Same detector, same distance from cube to detector.
• Same room temperature throughout (else the surroundings change).

Reverse experiment for absorption. Two metal plates (one matt black, one shiny silver) are placed equidistant from a radiant heater (e.g. a 60 W bulb). After a fixed time the matt-black plate has warmed up much more than the shiny one — best absorber matches best emitter.

Pick the right surface for the right job. AQA loves a four-mark 'explain why' question on these.

Solar water heater on a UK roof.

• Wants to absorb as much sunlight as possible → matt-black absorber plate.
• Glass cover keeps wind from cooling the plate.
• Hot plate transfers thermal energy to water in copper pipes behind.

Emergency 'space blanket'.

• Casualty's body is warmer than surroundings → wants to reduce IR loss to surroundings.
• Shiny silver surface reflects body's own IR back to the casualty (poor emitter) and is visible to rescuers.

Marathon foil blanket.

• After a race the runner is dehydrated and the wind cools them quickly. The foil reduces evaporative + radiative heat loss.

Vacuum flask (Thermos).

• Double-walled glass, vacuum between (stops conduction and convection).
• Both inner walls are silvered → reflects IR back inside → minimises radiative heat loss.

Teapot.

• Polished surface → poor emitter → tea stays hot longer.
• Modern stainless-steel kettles are sometimes black-coated inside to absorb heat from the element more efficiently.

Fridge back / heat-exchanger fins.

• Painted matt black → maximises IR emission → heat extracted from inside the fridge is radiated efficiently to the kitchen.

Buildings in hot climates.

• White/light-coloured walls and roofs reflect sunlight, so the interior stays cooler. (Used widely in Greece, Spain, Mexico.)

Survival in the cold (Arctic, expedition).

• Wear dark clothing to absorb maximum IR from the sun (when there is sun).
• Use foil-lined sleeping bags to reduce body-heat loss at night.

A perfect black body is an idealised object with two key properties:

1. It absorbs all the electromagnetic radiation that falls on it. None is reflected, none is transmitted.
2. Because perfect absorbers are also perfect emitters, it emits the maximum possible amount of radiation at every wavelength for its temperature.

The 'black' in the name refers to the absorption: at room temperature a perfect black body would look completely black because no light is reflected back to your eye.

Why study an idealised body? Real objects are not perfect — a piece of matt black card absorbs about 97% of visible light. But the black-body model is a useful starting point because the way real surfaces deviate from it is small and predictable.

Approximating a black body in the lab. A small hole in the side of a large hollow box approximates a black body. Any radiation entering the hole bounces around inside, hits the walls many times, and is almost entirely absorbed before it can escape — so the hole looks completely black even if the box walls are not.

Stars are good black bodies. Even though stars are luminous, their emission spectrum matches that of a black body closely. This lets astronomers measure the surface temperature of a star just from the colour of its light (see next section).

When the temperature of a body rises, two things happen to the radiation it emits.

1. Intensity rises sharply.

The total amount of energy emitted per second per square metre rises very steeply with temperature. (Mathematically it goes as $T^4$ — Stefan–Boltzmann law — but you do not need the equation at GCSE.) The qualitative idea is enough:

• Double the temperature (in kelvin) → emit roughly 16× more radiation per second.
• A red-hot poker (≈ 1000 K) emits hundreds of times more than the same poker at room temperature.

2. Peak wavelength shifts to shorter wavelengths (higher frequencies).

At every temperature there is a peak in the spectrum — the wavelength at which the most radiation is emitted. As the temperature rises:

• The peak wavelength decreases.
• At room temperature (≈ 300 K) the peak is in the far infrared — invisible.
• At about 1000 K the peak shifts toward red — an electric ring glows dull red.
• At about 5800 K (the Sun's surface) the peak sits in the visible band, near yellow-green.
• At very high temperatures (e.g. 30,000 K — a hot blue star) the peak shifts into the ultraviolet and the star looks blue-white.

Colour as a thermometer. Astronomers use the colour of a star to measure its surface temperature — a red star like Betelgeuse is ≈ 3500 K, a yellow-white star like our Sun is ≈ 5800 K, and a blue star like Rigel is ≈ 12000 K.

Everyday example — a kitchen kettle element. As you switch on the element, it starts at room temperature (no visible glow, all IR). Within seconds it begins to glow dull red, then bright orange. If left on much hotter, an old-style filament bulb glows white-yellow at about 2700 K.

Hotter → higher intensity, shorter peak wavelength Intensity → wavelength (nm)

Earth's temperature is set by a simple energy balance:

Rate of energy absorbed from the Sun = Rate of energy emitted to space → temperature steady.

Where the energy comes from. The Sun (≈ 5800 K) emits mostly visible light and near-IR. Some of this is reflected back into space by clouds, ice and pale ground surfaces; the rest is absorbed by Earth's surface and atmosphere.

Where the energy goes. The warm Earth (≈ 290 K) emits IR back to space, peaking in the mid- to far-IR. In a steady state, the energy radiated equals the energy absorbed — and Earth's temperature stays roughly constant.

What happens if the balance shifts?

• More absorption than emission → energy accumulates → Earth warms.
• Less absorption than emission → energy lost → Earth cools.

Greenhouse effect. Visible sunlight passes easily through the atmosphere and warms the surface. The surface then re-emits IR. Greenhouse gases (water vapour, CO₂, methane, nitrous oxide) absorb some of that outgoing IR and re-emit it back down to the surface. The result: less energy escapes to space, so Earth's temperature settles to a higher steady value than it would without the atmosphere.

Without any greenhouse effect, Earth's average surface temperature would be about -18 °C — far below freezing. With the natural greenhouse effect, it is about +15 °C — habitable.

Climate change (covered briefly in 4.5 atmospheric pressure and 4.6 here, in more detail in the Earth's atmosphere chemistry curriculum): adding more greenhouse gases (CO₂ from burning fossil fuels, CH₄ from livestock) increases absorption of outgoing IR. The new balance is reached at a higher surface temperature — current warming is consistent with this picture.

Day-night and seasonal variation.

• During the day, the side facing the Sun absorbs more energy than it emits → that part warms.
• At night, absorption ≈ 0 but emission continues → that part cools.
• Cloud cover blocks emission to space at night, so cloudy nights are warmer than clear nights.
• In summer the UK receives more solar energy per m² per day than in winter → summer temperatures are higher.

Star colour and temperature.

Star	Approx. temperature	Colour
Betelgeuse (red giant)	≈ 3500 K	Red
Sun	≈ 5800 K	Yellow-white
Sirius	≈ 9900 K	Blue-white
Rigel	≈ 12000 K	Blue

A hotter star emits more light overall and its spectrum peaks at shorter wavelengths.

Stove element / glow plug.

• Cold: invisible IR emission only.
• Warm (≈ 800 K): faint dull red — peak still in IR but tail of spectrum extends into red visible.
• Hot (≈ 1300 K): bright orange.
• Very hot (≈ 2000 K — e.g. tungsten filament): yellow-white.

Why a tungsten lamp wastes energy. A 60 W filament bulb at ≈ 2700 K has its peak emission in the near-IR, not the visible. Most of the energy goes into invisible IR (felt as heat). LED bulbs make light directly by electron transitions, avoiding this waste.

Why night sky cools. Clear sky lets IR from the ground escape directly to space (which is at about 3 K). A puddle on a clear, calm night can fall to several degrees below the air temperature and freeze even when the air is above 0 °C — radiative cooling.

Snowy ground. Fresh snow reflects most sunlight back to space (high albedo). Less absorbed → less re-emitted → colder local climate. This is one of the positive feedbacks that drives ice ages.

Earth from space. A satellite looking at Earth in IR sees the planet glowing brightly — its IR emission. Maps of this radiation are used to detect heat loss from cities and monitor sea-surface temperatures.