Ludwig Boltzmann was an Australian physicist who is well known in the world of physics and Chemistry. The main fields that make him a well known person in the field of science are the molecular motion of particles in which he proposes that molecules must have thermal energy on top of other forms of energy for them to move (Klein 45). He contributed immensely in statistical mechanical physics and statistical thermodynamics. By evaluating amount of energy in molecular bodies, his influence stretched further to cover molecular chemistry.
One of the most remembered and significant theory is the H-Theorem. The theorem tries to explain collision of molecules in a closed system. The main reason or purpose to present this theorem was to analyze the energy content in a body whose atoms and molecules are in motion. The main area that he focused on was the energy of the molecular bodies not he total body energy (en.wikipedia.org). For the theorem to hold, the following assumptions are made:
1. The collision of the atoms or molecules is unilateral.
2. The molecules/atoms undergo perfectly elastic collisions.
3. No energy is lost during the collision or transformed to other forms like sound and heat.
The density of the gas molecules is also low and uniform taking a value approximately equal to the gas density in the atmosphere.
The transport equation is represented as a balance equation thus is usually abbreviated as SZA which Boltzmann assumed to be an automatic assumption without even a valid name. From these assumptions, the H-theorem was analyzed to have the low density and one-dimensional collisions. The gas that he assumed to have such properties and near ideality characteristics was hydrogen. Therefore, in his experiment, he used hydrogen gas molecules to present his argument. In making use of hydrogen gas as the matter under experimentation, he was able to almost proof his theoretical idea experimentally.
In his almost breakthrough, Boltzmann almost successfully proved his point in thermodynamics. This led to development of thermodynamics laws and a new dawn in kinetic motion of molecules and atoms in chemistry. His idea also proved some earlier postulates of the kinetic motion of molecules and gases (Harven, 181).
So as to fully understand the main success and weakness of the theorem, let us have a look at the main experiment in detail.
The H-Theorem
This theorem was founded in the year 1872 and it explained the kinetic motion of gases. It was mainly based on hydrogen gas which is molecular and has characteristics which are almost those of an ideal gas. From the earlier outlined assumptions, the experiment was done assuming ideality.
The H function which is an integral of density is introduced. He made other assumptions that density was continuous and differentiable. The theorem was mainly based on these assumptions and probability making it to be highly criticized by later scientists as well as some scientists of the same time.
Critical analysis of the theorem by some scientists
1. Poincare critique. In the year 1889, only three years after the acceptance of H-Theorem, Poincare wrote an article criticizing the H-theorem. His main argument and reason to differ with the theorem was lack of explanation as to why heat can’t pass through a cold or hot body (Harven, 184). On my opinion, this question was valid since the theorem was not in a point to explain the question. From the contemporary analysis of some of these aspects affecting heat transfer, I can confidently claim that the question raised by Poincare was just but a lame excuse to oppose the theorem since heat transfer is a complex function dependent on temperature difference, type of material making the body and other factors like density. By the assumption that Boltzmann made, the conceptualization and simplification of kinetic energy theory was only simplified and modeled to vary with only a few variable thus was successful in predicting the outcome only for a modeled phenomenon.
2. Zamelo formulated a recurrence formula which scrutinized the H-theorem. It resulted in H-theorem taking another form and lastly solution to some assumptions. This recurrence theorem appears to support the H- theorem to some level and then correct some of the assumptions (Harven, 188). This shows that some of the scientists supported the H-theorem but tried to resolve some of the so many assumptions made.
The contemporary turn
Analyzing the H-theorem from a contemporary perspective, the theorem is more of a probability test than a concrete theorem. This is mainly exhibited by the assumptions made during its derivation and use. It is not always correct to assume that the SZA rule holds in all cases since in some special cases, other factors are more significant than others.
As an example, take a closed thermodynamic system. The density of molecules in the system may not be the same and uniformly distributed to have a homogeneous distribution. The energy content may also vary from one point of the system to another thus a general transportation factor which might vary with temperature. The other assumption made though it is not valid for any real system is the continuous density function which is differentiable. This makes the whole theorem appear not successful though it gives an insight of how molecular and gaseous motion and energy can be derived (Harven, 190).
The success of the theorem is only witnessed and evidenced by thermodynamics. This is mostly due to the evolution and derivation of laws of thermodynamics from the H-theorem. Considering the first law of thermodynamics, it is directly rooted in kinetic energy consideration of mechanics. The law is faced by criticism though it is still proven experimentally. The second law of thermodynamics, which explain adiabatic conditions of energy transfer expounds on some of the assumptions made in the original H –theorem. This is an indication that the contemporary learners have accepted the H-theorem making Boltzmann successful in his theory.
The third evidence that the theory has been partially successful is the incorporation of Boltzmann constant in many physics and chemistry calculations pertaining to heat within the molecules. This makes it more of a success than a failure since it is more accepted than rejected.
With the evidence from the discontents, the partial failure of the theorem can be attributed to the many assumptions made in the derivation of the theorem. The change in nature of the theorem to a probabilistic hypothesis is also a big blow to the theorem (Harven, 193).
In spite of all these, the theorem is was successfully accepted in the fields of physics and chemistry where it is widely applied in thermo physics and thermo chemistry to determine the amount of energy (energy content) in matter under consideration.
Harven B. Studies in History and Philosophy of Modern Physics: Boltzmann’s H-Theorem, its discontents and Birth of Statistical Physics. United Kingdom: Elsevier Limited. 2006. Print.
Klein, Martin. The Development of Boltzmann’s Statistical Ideas. Wien: Springer. 1973. Print.
