A gas is a collection of particles (molecules) that, to a first approximation, interact with one another solely through elastic collisions—in other words, through collisions that conserve both energy and momentum. If molecules were dimensionless, point-like objects, their thermal energy would be only that of linear motion in three dimensions—they would have only three degrees of freedom. In reality, molecules are more complicated. Even a simple monatomic one, such as helium, may be able to spin (because it has a finite dimension) and may, therefore, have more than three degrees of freedom. Multiatomic molecules can also vibrate, and this confers on them additional degrees of freedom.
At a given moment, some molecules have large kinetic energy, while others have little. However, over a sufficiently long period of time, each has the same average kinetic energy, <Wmoi >. This intuitive result is called the principle of equipartition of energy. What is not so immediately obvious is that the principle applies even to a collection of molecules with different masses: the more massive ones will have smaller average velocities than the lighter ones, but their average energy will be the same. According to this principle, the energy associated with any degree of freedom is the same. The instantaneous velocities have a Maxwellian distribution, as discussed in Section 2.18.
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