5.5 Black body radiation — Learn

Prerequisites: Section 5.1, especially infrared and the wave equation; Section 5.2, especially absorption and emission.

By the end of this section you can: explain that every object emits and absorbs radiation; describe how the radiation emitted changes with temperature; and explain why the temperature of an object can be steady.

1. Every object emits radiation

Every object emits electromagnetic radiation. The radiation comes from the motion of the particles inside the object. The warmer the object, the more radiation it emits.

A warm object emits mostly infrared radiation. Infrared is invisible, but a thermal camera can detect it. When an object becomes very hot, it also emits visible light. A piece of iron in a fire first glows dull red, then orange, then white.

An object can be a good absorber or a poor absorber of radiation. A black surface is a good absorber. A shiny surface is a poor absorber, because it reflects most of the radiation.

A good absorber is also a good emitter. A black surface absorbs infrared radiation well and emits it well. A shiny surface absorbs little and emits little.

2. Temperature and the radiation emitted

As the temperature of an object rises, two things happen to the radiation it emits.

It emits more radiation at every wavelength. The total intensity rises.
The wavelength of the most intense radiation becomes shorter.

A cool object emits most of its radiation at long infrared wavelengths. A hotter object emits more radiation, and its peak moves to shorter wavelengths. A very hot object, like the Sun, peaks in the visible range.

Worked example 1. A warm object emits most of its radiation at a wavelength of 8.0 μm. Calculate the frequency of this radiation.

\begin{aligned} f &= \frac{c}{\lambda} \\ &= \frac{3.0 \times 10^8}{8.0 \times 10^{-6}} \\ &= 3.75 \times 10^{13}\,\text{Hz} \\ &= 3.8 \times 10^{13}\,\text{Hz} \quad (2\ \text{significant figures}) \end{aligned}

3. Absorbing and emitting at the same time

Every object is absorbing radiation and emitting radiation at the same time.

If an object absorbs more than it emits, it warms up.
If an object emits more than it absorbs, it cools down.
If the two rates are equal, the temperature stays the same.

The Earth receives radiation from the Sun and emits its own infrared radiation. The Earth's average temperature is steady when these two rates are equal.

4. Changing the temperature

The figure shows how the radiation emitted by an object depends on its temperature. You can change the temperature of the object.

Predict first. Do not move the slider yet. Write down your answers.

As the temperature rises, does the peak of the curve move to the left or to the right?
As the temperature rises, does the total intensity go up or down?

Test. Move the slider and watch the curve. Find the temperature at which the peak reaches the visible range.

Explain. The Sun is much hotter than the Earth. Use the curve to explain why the Sun emits visible light while the Earth emits mostly infrared radiation. Write your answer in two or three sentences.

Watch out. Every object emits infrared radiation, even a cold one. Do not think that an object must be hot to emit anything. Also remember that a good absorber is a good emitter, so a black object cools quickly as well as warming quickly. A white or shiny surface is a poor absorber and a poor emitter.

5. Progress check

Return to the chapter problem. The observatory walls are painted white. Explain why they help to keep the inside cool on a sunny day, and what would change if they were painted black.

You should now be able to

explain that every object emits electromagnetic radiation;
state that the radiation emitted increases with temperature;
explain that the peak wavelength becomes shorter as the temperature rises;
use $f = \dfrac{c}{\lambda}$ for the peak radiation;
explain why a good absorber is also a good emitter;
explain how absorption and emission together set the temperature of an object.