Kinetic Theory and Flatlining of Polyatomic Gases
Kinetic Theory and Flatlining of Polyatomic Gases
Hello everyone at CNPS
I have not blogged in a while but still I am working on getting people interested in the rewriting of thermodynamics. Part of this path includes changing the way that we envision and teach kinetic theory. Just to remind you. In simplest context my first and second paper on kinetic theory throw out traditional kinetic theory of gases.
Discussion: Traditional Thermodynamics is based upon degrees of freedom and equipartition. Hence the energy of a gas is the addition of following:
1) Kinetic energy is purely translational: Specifically: kT/2 for each degree of freedom
2) Rotational energy is a separate degree of freedom than kinetic, i.e. another: kT/2
3) Vibrational energy of polyatomic gases, basically equal to: kT for each bond.
I realized that the walls might be thought of as massive rigid/stationary vibrating molecules which assert/impose their energetics onto colliding smaller gas molecules in sufficiently dilute gases. Moreover like any massive object asserting its energetics onto a much smaller object, the smaller object will take on both rotational and translational from the same impact. Accordingly both the rotational and translational energy will be determined by the energy imparted onto the smaller object.
As such we should rewrite kinetic theory under the following considerations:
1) Kinetic energy is translational plus rotational: Specifically: kT/2 along each of the three axis
2) Vibrational energy of polyatomic gases, basically equal to: kT for each bond.
One could rightfully argue that all we did was combine rotational energy with the translational and they would be right. But there is much more to this. The traditional considerations led to answers that only partially matched empirical/experiment accepted findings. This led the likes of Einstein thinking/claiming that quantum physics is needed to explain any discrepancies. And quantum physics then was employed, and explanations were claimed.
Unlike the traditional explanation, the explanation that I proposed matches empirical data almost precisely for 1 through 4 atom polyatomic gases that includes monatomic, diatomic and triatomic gases. Traditional kinetic theory is filled with exceptions even for these simple small gases
However just like traditional kinetic theory, my explanation did not explain why larger polyatomic gases do not adhere to either theory. Although my theory’s projected heat capacities were closer to accepted empirical findings than traditional theory was (for all gases), a discrepancy still was obvious for larger polyatomic gases.
Before returning to explaining empirical findings, there is another problem. When taught kinetic theory, we generally begin by thinking of a gas that hits a wall and experiences an elastic collision i.e. both momentum and kinetic energy are conserved. And then we go through a long analysis (including approximations) and arrived at the traditional kinetic theory.
However taking the new (my) perspective that massive relatively stationary large wall molecules impose their energy onto smaller gas molecules, means that intermolecular collisions no longer need to be elastic. In other words enclosed dilute gases seemingly obey conservation of energy, when the reality is that their kinetic energy (translational plus rotational) is enforced upon them.
Accordingly we are no longer handcuffed by collisions being elastic. If you think about it elastic collisions are the rarity in the real world. Heck even photon and electron collisions have been known to be inelastic.
This also implies that kinetic theory, ideal gas law, Avogadro’s hypothesis etc etc are all dependent upon idealistic dilute closed gas systems. Sufficiently dilute also implies relatively low pressure, hence gas-wall molecule collisions dominate over inter gas collisions (gas-gas).
Shortly after publication of the first paper I realize that perhaps flatling may be to blame. Note n” is just the number of atoms bonded together as a gas molecule AKA polyatomic number: Why does the discrepancy exist for n”>4? Consider that the gas molecule’s size influences the exchange of kinetic energy (gas’ translational plus rotational) with the wall molecule’s vibrational energy.
Small gas molecules (i.e. monatomic thru triatomic) tend to impact some relatively massive vibrating wall molecule hence the wall molecule imparts its momentum hence imposes a given kinetic energy (translational plus rotational as defined by kT/2) onto the impacting gas molecule. Understandably, small gas molecules i.e. n”<4, will tend to interact with the wall molecules cleanly.
This is not necessarily the case for larger molecules. Perhaps large vibrating wall molecules simply cannot cleanly pump kinetic energy onto such large gas molecules. It can be envisioned that elongated linear gas molecules and/or large gas molecules tend to “flatline” against the wall. The implication being that such large and/or elongated gas molecules tend to strike two or more (several) vibrating wall molecules at an instant, i.e. when some wall molecules are moving inwards, while their neighboring wall molecules are moving outwards, with respect to the wall as a whole.
Clearly the above alters the dynamics of any kinematic energy exchange. The expectation becomes that a large polyatomic gas molecule’s kinetic energy is no longer simply defined in terms of the vibrating wall molecule’s energy. Furthermore, the expectation still is that polyatomic gases still interact with any surrounding blackbody/thermal radiation.
Understandably the energy exchange between the walls and larger polyatomic would not be particularly clean hence will not be readily definable except to say that any net energy exchange is not readily definable and is probably zero (or close to it). Accordingly the energy changes of large polyatomic gases may be best approximated by change to their vibrational energy and this applies irrelevant as to the gas being in a closed or open system. Another was of visualizing is that large polyatomic gases simply absorb/emit radiation (thermal and/or blackbody) and attain their net energy changes this way. Their collisions with walls could certainly be considered as being inelastic.
Importantly the above considerations allows us to understand why the measured heat capacities of large polyatomic gases does approximate that of a gas, which only absorbs and emits radiation as their fundamental mechanism for net energy exchange, hence their mechanism of attaining thermal equilibrium. And by radiation I mean thermal and/or blackbody.
Understand inelastic collisions (gas-wall) means that radiation (thermal?) is given is given off. Is this radiation thermal? By thermal I mean photons that are readily absorbed by condensed matter resulting in vibrational energy within that matter i.e. thermal phonons. Whether this collision-induced radiation is absorbed by the wall as a phonon or become part of the radiation that surrounds the gas is not known. However it now becomes part of the system being in thermal equilibrium.
Similarly inter-gas collisions i.e. gas-gas, are not elastic! Herein momentum is conserved but kinetic energy is not hence radiation (generally photons) will be release due any inter-gas molecule collisions, thus making sure that energy is conserved. Remember kinetic energy is now translational plus any rotational energy!
Obviously this implies that the radiation that surround a system of gas molecules is a combination of blackbody radiation and other thermal radiation.
If anyone is interested my two papers on kinetic theory are now on Progress in Physics website. I really like this dealing with this group. They certainly have not published everything that I have sent them but they will consider unconventional theories if you can prove what you say. I of course used the empirical findings of others to prove my points in kinetic theory. And importantly the published papers are open sourced i.e. anyone can read/download for free. So thank you Progress in Physics for having an open mind and being open sourced!!!!
My recent (second paper) on the subject titled:
“Kinetic theory: Flatlining of Polyatomic Gases” (April 2018)
Link Progress in Physics (April 2018) :
As well as my first paper (July 2017) on kinetic theory
“A new perspective for kinetic theory and heat capacity” (July 2017)
Paper is found starting on page 166 in July 2017 Progress in physics: Link