By Kent W. Mayhew

The law of equipartition states that the total energy
of a gas is equally distributed among all of its degrees of freedom. Equipartition theorem is based upon the energy of a system being
defined by a set of *f* generalized coordinates (*q*_{1}….*q _{f}*) and their corresponding generalized momentum.

This leads to equipartition
theorem stateing that the mean energy for each independent quadratic term is ½ *kT*. For an ideal gas, the translational energy
of each gaseous molecule can be envisioned as being purely translational kinetic which contains three quadratic terms. Thus equipartition
states that the mean translational kinetic energy [Ekinetic] of an N molecule ideal gase is^{2,3}:

Ekinetic =3NkT/2 (6)

For *N* monatomic gas molecules the accepted vae for its total energy is defined by equation (6). Hence the isometric molar heat
capacity is 3R/2. Which is to illogically accept no consideration to rotational energy!!

The total mean vibrational energy [Evibrational] of a one-dimensional harmonic oscillator is the summation of the kinetic (kT/2) and potential (kT/2) energies, that being:

Evibrational=kT/2+k”T/2=kT (10)

For a diatomic gas the accepted degrees of freedom are: three degrees of freedom associated with translational energy, two degrees
of freedom with rotation and one degree accepted for vibration. Based upon this one would expect that isometric molar heat capacity
for a diatomic gas is 6R/2. However, the empirically proven value is 5R/2, which has led to the illogical act of the vibrational degree
of freedom being disregarded, thus enabling the theoretical value to equate to the empirical values. The accepted reasoning is that
vibrational energy at room temperatures makes negligible contributions to a gas’ heat capacity, which may strike some as odd since
vibrational and potential energy are the total contribution to the heat capacity of condensed matter, at room temperature. It is interesting
that no one has even queried this before.

In our new perspective (next page) we shall present a theory that has no such illogical
requirements at the above traditionally beheld theory obviously requires. Returning to the traditional accepted theory.

The
accepted theoretical isometric specific heats for monatomic through triatomic gases are given in Table 1:

For larger polyatomic gases consisting of n">2 atoms/elements
all three rotational degrees of freedom are now considered resulting in the degrees of freedom (3n”) being defined by:

3n”=3+3-(3n”-6) (11)

Equation (11) means that for larger polyatomic molecules that there are three degrees of freedom for translational and three degrees
of freedom for rotation plus (3n”-6) vibrational degrees of freedom.

Illogically, large linear molecules are treated slightly differently
with there being (3n”-5) vibrational degrees of freedom but only two degrees rotational of freedom, hence giving the same overall
value. Based upon degrees of freedom arguments the isometric molar heat capacity (Cv) for large polyatomic molecules would be:

Cv=3n”R/2 (12)

Although heat capacities of gases have been extensively studied throughout the 20^{th} century^{4,5,6}, no one has seen fit to challenge
the accepted traditional theory even though it is obviously filled with exceptions, all designed to make theory fit empirical
data. It is amazing how the sciences have gotten away with such continuous illogical fudge factoring all in the name
of making their pet theories fit empirical data.

In part 3 we will explain the grandiose mistake that is beheld in traditional kinetic theory and proovide a theory atht better fits all emperical data without relying upon an of the illogical fudge factoring that tradiational theory requires.

Copyright Kent W. Mayhew

Some referenced used herein

2. “Fundamentals
of Statistical and Thermal Physics”, F. Reif, McGraw-Hill, New York, 1965

3."Statistical Thermodynamics and Microscale Thermophysics",
V. Carey, Cambridge U 1999