‘Well, it’s very big!’ I hear you say. ‘There’s lots of fuel in there.’ Yes; yes, it is very big, and there is a lot of fuel. But that’s not why it’s such a long-term heat and light source. It is a little more complicated than that…
Here’s an interesting fact: kilogram for kilogram, the Sun puts out less energy than a human body. It is far less efficient than we are at generating power.
On the face of it, this is a little surprising – it’s an enormous flaming ball of gas that we couldn’t get anywhere near without disappearing in a puff of carbon. So how can it be so inefficient?
The answer lies in the fact that it is, indeed, a great big ball of gas and it behaves in a very similar way to gases on Earth. It turns out that gases are rather interesting and the way they behave under different conditions is predictable.
The Maxwell-Boltzmann curve
The distributions of speed and translational (movement) energy of the molecules in a gas are very similar if a gas is in equilibrium. The more molecules the gas contains, the fewer fluctuations in speed and energy distribution.
Essentially, this means that a certain percentage of gas molecules will tend to have a certain speed or energy level. This is best demonstrated using a Maxwell-Boltzmann graph:
This graph shows that there is a most-likely speed for any given gas molecule to have (and a similar curve exists for molecular translational energy). As long as the temperature of the gas is constant, the fraction of molecules with the most probable speed remains around the same (as does the fraction of molecules with any other speed).
(Note that molecules with a given speed may not be the same; their individual speeds keep changing as a result of collisions with other molecules, or the gas container.)
The graph has a long tail at higher speeds and energies: the likelihood of finding a molecule with a certain speed and energy decreases as speeds and energy levels increase. It’s the same for protons in the Sun.
This is the reason for the Sun’s longevity: the chance of two protons coming together in nuclear fusion is tiny. It has been estimated that it takes one proton five billion years to fuse with another proton. Most of the time, protons zip around in the Sun at relatively low speeds and energies, bouncing off one another and carrying on their merry way.
They are to be found in the ‘lumpy’ part of the distribution curve; the area with the ‘most likely’ speeds and energies. It is only when a proton (or molecule) falls into the tail end of the curve that it approaches the speed and energy required to undergo fusion.
Most of the Sun is too cold for fusion. When those very few protons in the tail end of the distribution curve do come together in fusion, they release large amounts of stored energy.
It is, therefore, extremely unlikely that fusion will occur in the Sun. However, it’s so massive that its total energy output is enormous so it is pretty hot. And bright. If the distribution patterns of speed and energy were different, the Sun could have burned out millennia ago, or may never have got very hot at all.
Gases are predictable
The speed distribution of a gas depends on the mass of the molecule, but the translational energy distribution is the same for all gases at the same temperature.
In other words, the larger the molecules’ mass, the slower their speed; so the speed distribution will be affected by molecule size. However, the molecules’ mass has no effect on the energy distribution – it’s the same for all gases at a fixed temperature.
- The speed and energy of a gas’s molecules increase as the temperature increases, as long as the volume is fixed.
- The molecules’ energy is unaffected by a change in speed at a fixed temperature and volume.
- The speed and energy are unaffected by an increase in volume, at a fixed temperature.
These properties have been extremely useful in the development of technology – and led to the invention of a simple but quite marvellous fire-starting device: the fire piston.
Because compressing gases leads to an increase in temperature, if you do it quickly enough you can ignite flammable material without any need for sparks or traditional fuel. An old-fashioned fire piston is still useful today for campers, climbers and other such adventurers. It’s small and easy to use: take a long, thin cylinder, a rod or piston, and place some flammable material in the bottom of the cylinder. Plunge the piston down rapidly, and watch the material ignite. This video shows you how to make one, which I will do at some point:
Science in action. It’s marvellous!