Abstract
Around the year 1900, J.H. Jeans suggested that the `abnormal'
specific heats observed in diatomic gases, specifically the lack
of contribution to the heat capacity from the internal vibrational
degrees of freedom, in apparent violation of the equipartition
theorem, might be caused by the large separation between the time
scale for the vibration and the time scale associated with a
typical binary collision in the gas. We consider here a simple 1-D
model, and show how, when these time scales are well separated,
the collisional dynamics is constrained by a many-particle
adiabatic invariant. The effect is that the collisional energy
exchanges between the translational and the vibrational degrees of
freedom are slowed down by an exponential factor (as Jeans
conjectured). A metastable situation thus occurs, in which the
fast vibrational degrees of freedom effectivly do not contribute
to the specific heat. Hence, the observed `freezing out' of the
vibrational degrees of freedom could in principle be explained in
terms of classical mechanics. We discuss the phenomenon
analytically, on the basis of an approximation introduced by
Landau and Teller (1936) for a related phenomenon, and estimate
the time scale for the evolution to statistical equilibrium. The
theoretical analysis is supported by numerical examples.
Original language | English |
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Journal | Journal of Statistical Physics |
Volume | 94 |
Pages (from-to) | 871-891 |
ISSN | 0022-4715 |
Publication status | Published - 1999 |