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## Statistical thermodynamicsIn thermodynamics, ## Additional recommended knowledge
## OverviewThe essential problem in statistical thermodynamics is to determine the distribution of a given amount of energy ## HistoryIn 1738, Swiss physicist and mathematician Daniel Bernoulli published 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. 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 ## Classical thermodynamics vs. statistical thermodynamicsAs 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 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. ## FundamentalsCentral topics covered in statistical thermodynamics include: - Microstates and configurations
- Boltzmann distribution law
- Partition function
- Thermodynamic equilibrium - thermal, mechanical, and chemical.
- Internal degrees of freedom - rotation, vibration, electronic excitation, etc.
- Heat capacity – Einstein solids, polyatomic gases, etc.
- Nernst heat theorem
- Fluctuations
- Gibbs paradox
- Degeneracy
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 *k*is Boltzmann's constant 1.38066×10_{B}^{−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). ## RelatedIn 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**^**On history of fundamentals of statistical thermodynamics (section 1.2)**^**Schrodinger, Erwin (1946).*Statistical Thermodynamics*. Dover Publications, Inc..__ISBN 0-486-66101-6__.**^**Mahon, Basil (2003).*The Man Who Changed Everything – the Life of James Clerk Maxwell*. Hoboken, NJ: Wiley.__ISBN 0-470-86171-1__.**^**Perrot, Pierre (1998).*A to Z of Thermodynamics*. Oxford University Press.__ISBN 0-19-856552-6__.**^**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__
Categories: Thermodynamics | Statistical mechanics |
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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. |