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David Christian's Maps of Time has this to say about the period during which the first stars started to form from the diffuse clouds of hydrogen and helium that then made up the universe:

Under the pull of their own gravity, the clouds of hydrogen and helium began to collapse in on themselves...As gravity packed each cloud into ever smaller spaces, pressure built up in the center. Increasing pressure means increasing temperatures, and so, as they shrank, each gas cloud began to heat up (~Kindle location 1469).

The part I'm working on understanding is "Increasing pressure means increasing temperatures." Does the pressure itself cause the molecules to heat up? Or is it the kinetic energy that the particles pick up as gravity pulls them towards the center of the cloud? Or is the phenomenon here something other than increased energy per unit mass?

Of course, once the nuclear chain reaction gets started in the star it's not hard to figure out where the energy comes from. I'm talking about before that.

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This is basic thermodynamics.

When you compress a gas, you inject energy into it. Think of the pump you use to inflate the tires on your bike. It takes some force to move the piston, right? That effort is not wasted, but goes directly into the air in the pump. Now the air has more energy.

But what happens to a gas when you put energy into it? It's molecules jiggle around faster. Well, faster jiggling is basically the definition of higher temperature. By putting more energy into the gas, you raise its temperature.

You can actually tell that the bike pump is getting warmer if you pump quickly and forcefully - this is something you can experience yourself.

Same with stars - the whole star is the "bike pump", and gravity is the one who's pushing the piston. Due to compression (shrinking) under gravity, the gas gets hotter and hotter. It turns out a star has A LOT of gravitational energy, so the gas can get VERY hot.

In your terms, yes, it's the acceleration that molecules experience falling into the gravity well of the star that makes them move faster. Faster moving molecules = higher temperature. Pretty straightforward phenomenon, really.

Historically, gravitational compression was thought to be the main source of energy for the stars, before the discovery of nuclear physics. Helmholtz and Lord Kelvin proposed this hypothesis in the 1800s.

The pressure-temperature relation of any gas was originally known as the Gay-Lussac law. Now we know it's just a particular case of more general phenomena (ideal gas law) tying together pressure, temperature, volume, and various kinds of energy.

A spectacular application of the p-T relation is the so-called "fire piston" or "fire syringe", which can ignite small pieces of cotton or paper by just hitting a piston really hard (extremely strong compression = big temperature rise). Search Youtube for some videos like this one:

https://www.youtube.com/watch?v=4qe1Ueifekg

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  • $\begingroup$ Here's a thought that occurred to me this morning. You've pointed out that when you bump air into a tire you get the molecules moving faster (more energy per molecule). What if I use a pump to remove the air from a tire (or whatever else). In that case I'm still doing work. Does anything happpen to the energy per molecule of those molecules that remain in the tire? What if, instead of a tire, I pump the air out of some rigid container? $\endgroup$
    – kuzzooroo
    Commented Mar 20, 2015 at 13:27
  • $\begingroup$ When pumping air out of a container, you're doing work, of course, but that work is against the whole rest of Earth's atmosphere, not against the air in the tire. It's really simple: your work goes into that side of the pump which has the greater pressure. $\endgroup$
    – Florin Andrei
    Commented Mar 20, 2015 at 18:13
  • $\begingroup$ So no first order effect on the air remaining in the tire, right? $\endgroup$
    – kuzzooroo
    Commented Mar 20, 2015 at 20:30
  • $\begingroup$ If you're sucking out of the tire with the pump, then the air in the tire is doing mechanical work on the piston, actually. $\endgroup$
    – Florin Andrei
    Commented Mar 20, 2015 at 23:48
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Interesting question that demonstrates "thinking through". I will give my shot on trying to explain it by my perception.

The first part holds the ideal gas laws for true, which to a certain point will hold. When the star cloud obeys the laws of ideal gasses the temperature of a gas can be described as: $$PV = nRT = NkT$$

Here is $P$ the pressure, $V$ the volume, $T$ the temperature, $N$ Avogadro's number and $k$ the Boltzmann constant. ($n$ is the number of moles and $R$ the gas constant).

This relation shows that when a star cloud collapses under its weight the volume decreases and thus pressure and/or temperature increases. This relation is based on the statistical relation that many atoms are packed together, but not physically interact. The increasing temperature and therefore increasing kynetic energy of the atoms is caused by the increasing chance that the atoms collide with each other more frequently when the volume decreases. The ideal gas law explains the first increase in temperature by increase of the kynetic energy of the atoms.

The chain reaction first appears when the ideal gas law doesn't apply anymore. The further collapse of a large star cloud causes the center of the cloud to reach those levels of pressure, that atoms start to physically interact and the gas becomes a plasma. First then the nuclear fusion will start.

Hope this answers your question.

Kind regards, MacUserT

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