Black body radiation

Physics · Waves. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Every body emits and absorbs infrared radiation, whatever its temperature. The hotter the body, the more infrared radiation it emits in a given time.

A perfect black body absorbs all the radiation that falls on it. It reflects none and transmits none. A good absorber is also a good emitter, so a perfect black body is the best possible emitter too.

As a body gets hotter, the intensity of every wavelength it emits increases, and the shorter wavelengths increase most. Its temperature depends on a balance: it warms up if it absorbs radiation faster than it emits it, and cools down if it emits faster than it absorbs.

Rules to remember

All bodies emit and absorb infrared radiation, at any temperature.
Hotter body: more radiation emitted per second.
Perfect black body: absorbs all incident radiation; best possible emitter.
Higher temperature: greater intensity, and the peak of the emitted radiation moves to shorter wavelengths.
Constant temperature: rate of absorbing radiation = rate of emitting radiation.
Earth's temperature depends on the rates at which radiation is absorbed, emitted and reflected back into space.
Matt black surfaces are the best absorbers and emitters; shiny surfaces are the worst.

Common mistake

Students think a body at constant temperature has stopped emitting or absorbing radiation. It is still doing both, at equal rates.

Worked example

Two stars are seen in the night sky. One looks red and the other looks blue-white. Which star has the hotter surface?

A hotter body emits a greater proportion of its radiation at shorter wavelengths.
Blue light has a shorter wavelength than red light.
So the blue-white star emits more of its radiation at short wavelengths and is the hotter one.

Answer: The blue-white star is hotter.

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