Why is the Sun hot?

An image of the surface of the Sun. We know the Sun is hot, but why? Image from the NASA Solar Dynamics Observatory.

Some questions are so obvious that it seems barely necessary to ask them. But in fact the reason the Sun is hot is not because of the nuclear fusion taking place at its heart. Or at least not only for that reason. The main reason the Sun is hot is because it is an excellent thermal insulator.

What? Yes, that is what I said. Although the Sun produces a phenomenal amount of energy, it is also phenomenally large and the energy has to travel stupendous distances from the core to the surface to escape which insulates the core, allowing a tremendous build up of temperature.

I learned this while reading Ben Craven’s superbly browsable web pages wherein he compares the Sun with another heat-generating object: a human body. He shows that per unit mass, a human body generates more than 6000 times more energy than the Sun! But in our bodies the heat can be quickly lost because the surface of our bodies is not so far from our warm ‘core’. I have taken the liberty of summarising Ben’s more detailed calculation:

Mass of the Sun. Close to 2 x  10³⁰ kg (from wiki).

Total power output of Sun.  3.87 × 10²⁶ watts (from wiki).

Mass of a person. 80 kg (I should diet I know)

Power output of a person. A typical adult eats 2000  kcal a day, or about 8.6 × 10⁶ joules. Divided by the number of seconds in the day (=60 x 60 x 24 = 86400), this gives an average power of  about 100 W.

Power output per kilogram. If we divide the total power output by the mass in each case we get

• 0.00019 W kg^-1 for the Sun and
• 1.25 W kg^-1  for a human being.

Now I quote this here because I was so shocked by the result. Seeing the images of the broiling mass of gas on the Sun’s surface, it seemed obvious that reason for the Sun’s high surface temperature was the phenomenal power released in the Sun’s core. And it is. But it is not until one makes some calculations that one realises that the physics is a little more accessible than one previously thought.

Or as the rapper Fizzy Willow puts it:

Don’t give me no suss or saz,
Or I will get numerical on your ass.

Tags: Amazing fact, Ben Craven, Power density