Statistical thermodynamics



In Ludwig Boltzmann, much of which was collectively published in Boltzmann's 1896 Lectures on Gas Theory.[1]   Boltzmann's original papers on the statistical interpretation of thermodynamics, the 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.[2] 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 heat is simply the kinetic energy of their motion.

In 1859, after reading a paper on the diffusion of molecules by 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, 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.[4]

Classical thermodynamics vs. statistical thermodynamics

As an example, from a thermodynamic parameters of a system, such as temperature and pressure, are interpretable in terms of the parameters descriptive of such constituent atoms and molecules.[5]

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 statistical entropy is defined as:

S = k_B \ln \Omega \!

where

kB is Boltzmann's constant 1.38066×10−23 J K−1 and
\Omega \! 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).

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.

See also

References

  1. ^ On history of fundamentals of statistical thermodynamics (section 1.2)
  2. ^ Schrodinger, Erwin (1946). Statistical Thermodynamics. Dover Publications, Inc.. ISBN 0-486-66101-6. 
  3. ^ Mahon, Basil (2003). The Man Who Changed Everything – the Life of James Clerk Maxwell. Hoboken, NJ: Wiley. ISBN 0-470-86171-1. 
  4. ^ Perrot, Pierre (1998). A to Z of Thermodynamics. Oxford University Press. ISBN 0-19-856552-6. 
  5. ^ Nash, Leonard K. (1974). Elements of Statistical Thermodynamics, 2nd Ed.. Dover Publications, Inc.. ISBN 0-486-44978-5. 

Further reading

  • Ben-Naim, Arieh (2007). Statistical Thermodynamics Based on Information.  ISBN 978-981-270-707-9
  • Boltzmann, Ludwig; and Dieter Flamm (2000). Entropie und Wahrscheinlichkeit.  ISBN 978-3817132867
  • Boltzmann, Ludwig (1896, 1898). Lectures on gas theory.  translated by Stephen G. Brush (1964) Berkeley: University of California Press; (1995) New York: Dover ISBN 0-486-68455-5
  • Gibbs, J. Willard (1902). Elementary principles in statistical dynamics. New York. ; (1981) Woodbridge, CT: Ox Bow Press ISBN 0-918024-20-X
  • Landau, Lev Davidovich; and Lifshitz, Evgeny Mikhailovich. Statistical Physics.  Vol. 5 of the Course of Theoretical Physics. 3e (1976) Translated by J.B. Sykes and M.J. Kearsley (1980) Oxford : Pergamon Press. ISBN 0-7506-3372-7
  • Reichl, Linda E (1980). A modern course in statistical physics. London: Edward Arnold.  2e (1998) Chichester: Wiley ISBN 0-471-59520-9
 
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Statistical_thermodynamics". A list of authors is available in Wikipedia.