Everything about Statistical Thermodynamics totally explained
In
thermodynamics,
statistical thermodynamics is the study of the microscopic behaviors of
thermodynamic systems using
probability theory. Statistical thermodynamics, generally, provides a molecular level interpretation of thermodynamic quantities such as
work,
heat,
free energy, and
entropy. Statistical thermodynamics was born in 1870 with the work of Austrian physicist
Ludwig Boltzmann, much of which was collectively published in Boltzmann's 1896
Lectures on Gas Theory.
Boltzmann's original papers on the statistical interpretation of thermodynamics, the
H-theorem,
transport theory,
thermal equilibrium, the
equation of state of gases, and similar subjects, occupy about 2,000 pages in the proceedings of the Vienna Academy and other societies. The term "statistical thermodynamics" was proposed for use by the American thermodynamicist
Willard Gibbs in 1902. According to Gibbs, the term "statistical", in the context of mechanics, for example
statistical mechanics, was first used by the Scottish physicist
James Clerk Maxwell in 1871.
Overview
The essential problem in statistical thermodynamics is to determine the distribution of a given amount of energy
E over
N identical systems. The goal of statistical thermodynamics is to understand and to interpret the measurable macroscopic properties of materials in terms of the properties of their constituent particles and the interactions between them. This is done by connecting thermodynamic functions to quantum-mechanic equations. Two central quantities in statistical thermodynamics are the
Boltzmann factor and the
partition function.
History
In 1738, Swiss physicist and mathematician
Daniel Bernoulli published
Hydrodynamica which laid the basis for the
kinetic theory of gases. In this work, Bernoulli positioned the argument, still used to this day, that gases consist of great numbers of molecules moving in all directions, that their impact on a surface causes the gas pressure that we feel, and that what we experience as
heat is simply the kinetic energy of their motion.
In 1859, after reading a paper on the diffusion of molecules by
Rudolf Clausius, Scottish physicist
James Clerk Maxwell formulated the
Maxwell distribution of molecular velocities, which gave the proportion of molecules having a certain velocity in a specific range. This was the first-ever statistical law in physics. Five years later, in 1864,
Ludwig Boltzmann, a young student in Vienna, came across Maxwell’s paper and was so inspired by it that he spent much of his long and distinguished life developing the subject further.
Hence, the foundations of statistical thermodynamics were laid down in the late 1800s by those such as
James Maxwell,
Ludwig Boltzmann,
Max Planck,
Rudolf Clausius, and
Willard Gibbs who began to apply statistical and quantum atomic theory to ideal gas bodies. Predominantly, however, it was Maxwell and Boltzmann, working independently, who reached similar conclusions as to the statistical nature of gaseous bodies. Yet, one most consider Boltzmann to be the "father" of statistical thermodynamics with his 1875 derivation of the relationship between entropy
S and multiplicity
Ω, the number of microscopic arrangements (microstates) producing the same macroscopic state (macrostate) for a particular system.
Classical thermodynamics vs. statistical thermodynamics
As an example, from a
classical thermodynamics point of view we might ask what is it about a
thermodynamic system of gas molecules, such as
ammonia NH
3, that determines the
free energy characteristic of that compound? Classical thermodynamics doesn't provide the answer. If, for example, we were given spectroscopic data, of this body of gas molecules, such as
bond length,
bond angle,
bond rotation, and flexibility of the bonds in NH
3 we should see that the free energy couldn't be other than it is. To prove this true, we need to bridge the gap between the microscopic realm of atoms and molecules and the macroscopic realm of classical thermodynamics. From physics,
statistical mechanics provides such a bridge by teaching us how to conceive of a thermodynamic
system as an assembly of
units. More specifically, it demonstrates how the
thermodynamic parameters of a system, such as temperature and pressure, are interpretable in terms of the parameters descriptive of such constituent atoms and molecules.
In a bounded system, the crucial characteristic of these microscopic units is that their energies are
quantized. That is, where the energies accessible to a macroscopic system form a virtual continuum of possibilities, the energies open to any of its submicroscopic components are limited to a discontinuous set of alternatives associated with integral values of some
quantum number.
Fundamentals
Central topics covered in statistical thermodynamics include:
Lastly, and most importantly, the formal definition of
entropy of a
thermodynamic system from a
statistical perspective is called
statistical entropy is defined as:
»
where
» kB is
Boltzmann's constant 1.38066×10
−23 J K
−1 and
is the number of
microstates corresponding to the observed thermodynamic macrostate.
A common mistake is taking this formula as a hard general definition of entropy.
This equation is valid only if each microstate is equally accessible (each microstate has an equal probability of occurring).
Boltzmann Distribution
If the system is large the
Boltzmann distribution could be used (The Boltzman distribution is an approximate result)
»
Related
In the late 19th century,
Ladislaus von Bortkiewicz, a Russian-born statistician, intrigued by the heating of cannons as they were fired, attempted to statistically predict the overheating of an artillery battalion. His few trials showed that the metallic composition of cannon barrels in Poland varied too greatly at the time to effectively predict the outcomes of an entire battalion.
Further Information
Get more info on 'Statistical Thermodynamics'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://statistical_thermodynamics.totallyexplained.com">Statistical thermodynamics Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
