April 24, 2002

The Dancing Molecules

In the late 19th century a heated discussion went on about the temperature distribution in vertical columns of gas. L.Boltzmann (1) tried to prove with his calculations that a vertical column of gas under equilibrium conditions would have to show equal temperatures over height. Otherwise the construction of A PERPETUUM MOBILE OF THE SECOND KIND would be possible.

J.C.Maxwell (2) agreed. Based on the same assumption he calculated the speed distribution of molecules. He found that it would be identical for different gases and depend only on their temperature.

But there was a lonely dissenting voice. J. Loschmidt (3) disagreed. He felt, that gravity would cause a stratification of temperatures, cold at the top, warmer at the bottom. But Loschmidt died in 1895.

Throughout the following years theoretical arguments were put forth, but they changed over time. Only an equal temperature over height was consistent with the SECOND LAW OF THERMODYNAMICS and as long as the theories showed such a result, they were accepted nearly universally as correct. A good summary is given by A.Trupp (4).

Did anybody ever measure this temperature distribution? I am not aware of any published results. If you are, please let me know.

When I started with measurements, I took the following approach: I look at a container filled with a gas with such a low pressure that the free path is longer than the vertical distance of the walls:

With an assumed inner pressure of .0001 mbar, the free length of the molecules at room temperature is about .6 meter. If the vertical height of our container is .1 meter, a molecule flying between the upper and lower walls would bounce back and forth between these walls with hardly ever hitting another molecule. On its downward path it would be accelerated by the influence of gravity, increasing its speed. On the upward path the opposite happens; the speed of the molecule is reduced.

But the speed of a molecule corresponds to its temperature. We also know that a molecule bouncing off a wall leaves the wall, on the average, with the temperature of this wall. If initially the walls had the same temperature, then the upper wall would lose energy as it accelerated the arriving "slow" molecules while the lower wall would receive an equivalent amount. The upper wall would get colder, the lower one warmer as energy would be transferred from the top wall to the bottom one.

This thought experiment seemed to indicate that a temperature gradient would slowly would build up.If we wait long enough until we reach equilibrium conditions, then the upper wall would have to show a lower temperature than the lower wall, as it gets hit by molecules with a slower speed than the lower wall.

My BOOK will describe this happening in more detail. It points out that this process would take place not only in a rarified gas but also in a dense one. Here a molecule would bounce from molecule to molecule and would hit a wall only rarely. Still, the stratification of temperatures, cold at the top and warm at the bottom would take place just the same. Our main interest, is of course, to find out, what size of temperature difference we can expect to get. This I will discuss under TEMPERATURE DIFFERENCE IN THE GRAVITATIONAL FORCE FIELD.