Monday, February 1,2010
(The Kinetic Theory of Gases)
The Connection between the Macroscopic and the Microscopic World (Continued)
How does the distribution change, if the gas
made of more massive particles?
while we keep T fixed, leads to a decrease in the most probable speed.
Heavier particles will move more slowly, on average, for a given energy (temperature).
We should thus expect the curves to shift toward the left when we pick heavier gases.
The figure below illustrates this behavior for He, Ne, Ar and Xe.
Maxwell-Boltzmann Molecular Speed
Distribution for Noble Gases
of the Maxwell-Boltzmann distribution on both temperature and the
mass of the particles has direct implications for a planet's (or moon's) ability to retain an
atmosphere. Por a given temperature and gas species, one can compute the root-mean
square-speed. If this speed is larger than the escape speed from the planet, then that
of gas will be lost over time.
Example 1 We can compute this for
molecules at the current average temperature
the Earth (at the surface), 287K.
According to this very simplistic consideration, it appears as though
Atmospheric escape, however, does not happen at the surface, but high up in] the
atmosphere, in a region called the exosphere. The temperature there can be larger
with respect to the surface.