Statistical thermodynamics

Statistical thermodynamics is a branch of thermodynamics that provides a molecular level interpretation of thermodynamic quantities as work, heat, and entropy. 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, i.e. 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 physician 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. Predominately, however, it was Maxwell and Boltzmann, working independently, who reached similar conclusions as to the statistical nature of gaseous bodies. Yet, 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 microscopic arrangements (microstates) producing the same macroscopic state (macrostate) for a particular system.

Theories

Formal Definition of entropy of a system:

S = k_B \; \log W

where $k_B \,$ is Boltzmann's constant $1.38066 \times 10^{-23} J K^{-1} \,$

References

External links

Statistical Thermodynamics - Historical Timeline
Major Equations and derivations In statistical Thermodynamics

thermodynamics | Statistical mechanics

Termodinamika statistik | ترمودینامیک آماری