Dave- That's an interesting question that can stand alone, so I've taken it out of the long follow-up thread.
What you're noticing is that gases tend to float up away from the earth, while liquids and solids tend to fall. The cycle of water evaporating and the falling back as rain or snow is a familiar example.
Here's what changes about the gravitational attraction to the earth of a water molecule as it leaves the liquid and goes off as vapor: nothing
(Strictly speaking, the slight gain in potential energy as it loses contact with its neighbors causes a tiny relativistic increase
in its gravitational mass as it becomes vapor, but that's negligible.)
So why does the liquid hang around in a pool on the surface and the vapor float around up in a few-km thick atmosphere? The answer lies not in any change in gravity but rather in a completely different principle, the one that determines what sort of equilibrium states form. Nature seems to become completely indifferent to which particular quantum states it's in. In practice, that means things move toward conditions with by far the most states. We keep track via entropy
, the log of the number of states. The number of states of two things is the product of their separate numbers, so the entropy is just the sum of the separate entropies. (OK, with entangled exceptions, if any of you sophisticates are reading.)
How can the water maximize its entropy? Obviously that would be by breaking up into separate molecules and running around over a big volume. However, as the molecules go up, they gain gravitational potential energy, and that energy comes from somewhere. Taking energy out of things lowers their entropy. So the vapor floats to a height where there's an even tradeoff between gaining entropy by exploring a big volume and making others lose entropy by swiping their energy.
What about the liquid? Wouldn't all those molecules lose a lot of entropy by sticking together? Yes- but they can release energy when they do, because there's a negative potential energy of their sticking interactions. That released energy makes entropy in the neighbors.
So what determines if the water forms liquid or gas? That depends on how much entropy the neighborhood gains per energy it gets. The more it gains, the more it drives the water into the liquid. We need a name for an important property like that: we name it
1/T=dS/dU, where T is the absolute temperature, S is the entropy in some standard units, and U is the internal thermal energy. (To get a little more precise about all this, one should read a beginning thermal physics text, e.g. the one by Tom Moore.) So when the neighborhood is cold, it sucks energy out and leaves the water as a liquid- or even a solid when it's colder. Lumps like that don't gain nearly as many new states by jumping around as separate individual molecules do, so the lumps don't and the molecules do.
(published on 08/01/2011)