By Kent W. Mayhew

Maxwell & Kinetic Theory

The conceptualization of a gaseous system’s kinematics originated in the writings of the 19^{th} century
greats. In 1875, Maxwell wrote:

“*The kinetic energy of the molecule may be regarded as made up of two parts--that of the mass of the
molecule supposed to be concentrated at its centre of mass, and that of the motions of the parts relative to the centre of mass. The
first is called the energy of translation, the second that of rotation and vibration. The sum of these is the whole energy of motion
of the molecule.*

*The pressure of the gas depends, as we have seen, on the energy of translation alone. The specific heat depends on
the rate at which the whole energy, kinetic and potential, increases as the temperature rises. *

* Clausius had long ago pointed
out that the ratio of the increment of the whole energy to that of the energy of translation may be determined if we know by experiment
the ratio of the specific heat at constant pressure to that at constant volume. *

*He did not, however, attempt to determine à priori
the ratio of the two parts of the energy, though he suggested, as an extremely probable hypothesis, that the average values of the
two parts of the energy in a given substance always adjust themselves to the same ratio. He left the numerical value of this ratio
to be determined by experiment. *

*In 1860 I investigated the ratio of the two parts of the energy on the hypothesis that the molecules
are elastic bodies of invariable form . I found, to my great surprise, that whatever be the shape of the molecules, provided they are
not perfectly smooth and spherical, the ratio of the two parts of the energy must be always the same, the two parts being in fact
equal. This result is confirmed by the researches of Boltzmann, who has worked out the general case of a molecule having n variables.”*

It is interesting to note Maxwell’s surprise at the ratio of energies (the translational motion and the rotational and/or vibrational) being equal, as not even he expected this traditionally accepted result. This was followed by the work of Boltzmann with his conceptualization of statistical ensembles, led to the 20th century understanding of the determination of molecular energy using statistical analysis and equipartition. It is currently accepted that the specific heat of gases can be best explained in terms of equipartition theory, and degrees of freedom.

In Part two of this blog we will investigate this further, showing that Maxwell was right to express his concerns concerning accepted kinetic theory. In Part 3 we will present a theory that actually fits the empirical data without the needs of the illogical exceptions/fudge factors etc that burden the accepted traditional degrees of freedom based arguments.

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