Starlight and temperature.

Step 1 of 6

The colour of heat

You cannot send a thermometer to a star, but you can take its light apart. In the Scene a lump of tungsten sits in an open furnace, glowing red at 950 K. Every warm body gives out electromagnetic waves, and what it gives out depends almost only on its temperature, not on the material: such a body is called a blackbody, because it absorbs all the light that falls on it. Stars are very close to blackbodies.

Change Temperature of the lump and watch the colour change: below about 800 K it does not glow at all, and then it goes red, orange, yellow and white.

Step 2 of 6

Wien’s law

Show the whole spectrum shows the whole curve, including the part the eye cannot see: how much light the lump gives out at each wavelength. The curve has a peak, and Wien’s displacement law says where:

$\lambda_{\max} = \frac{b}{T}, \qquad b \approx 2.90 \times 10^{-3}\ \mathrm{m \cdot K}$$\lambda_{\max} =$$\frac{b}{T}, \qquad b \approx$$2.90 \times 10^{-3}\ \mathrm{m \cdot K}$⁠

Here $T$⁠ is in kelvin. The peak goes inversely with the temperature: a body twice as hot gives out mostly at half the wavelength. Temperature of the lump is locked at 1300 K.

Step 3 of 6

Hotter and shorter

Predict what will happen to the curve as the lump heats up, then compare with the reading of the peak.

Step 4 of 6

One micrometre

Now turn Wien’s law round: if you know where the peak is, you know the temperature. That is how a star’s temperature is measured.

Step 5 of 6

The fourth power

As the lump heats up, the curve does not only move: it also grows enormously. The area under it is the total power each square metre gives out, and the Stefan–Boltzmann law says how much:

$P = \sigma T^4, \qquad \sigma \approx 5.67 \times 10^{-8}\ \mathrm{W/(m^2 \cdot K^4)}$$P =$$\sigma T^4, \qquad \sigma \approx$$5.67 \times 10^{-8}\ \mathrm{W/(m^2 \cdot K^4)}$⁠

The power reading is beside the Scene. A whole star’s power is $P$⁠ times its surface area, $4\pi R^2$⁠: a star can be bright because it is hot, or because it is huge.

Step 6 of 6

The Sun’s temperature

The furnace goes only up to 3000 K. Show the whole spectrum now adds, as a dashed line, the Sun’s curve for comparison. Use its peak.