Ludwig Boltzmann

Ludwig Eduard Boltzmann ( Vienna , Austria-Hungary , February 20 , 1844 – Duino near Trieste , September 5 , 1906 ) was an Austria n Physicist famous for the invention of Statistical Mechanics .

Boltzmann's most important scientific contributions were in Kinetic Theory , including the Maxwell-Boltzmann Distribution for molecular speeds in a gas. In addition, Maxwell-Boltzmann Statistics and the Boltzmann Distribution over energies remain the foundations of Classical statistical mechanics. They are applicable to the many Phenomena that do not require Quantum Statistics and provide a remarkable insight into the meaning of Temperature .

Much of the Physics establishment rejected his thesis about the reality of Atom s and Molecule s — a belief shared, however, by Maxwell in Scotland and Gibbs in the United States ; and by Most Chemists since the discoveries of John Dalton in 1808. He had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient Theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of Colloid al suspensions (1908-1909) confirmed the values of Avogadro's Number and Boltzmann's Constant , and convinced the world that the tiny particles Really Exist .

To quote Planck , ''The Logarithm ic connection between Entropy and Probability was first stated by L. Boltzmann in his Kinetic Theory of gases.'' This famous formula for entropy

S

is

:

S = k \; \log W

where

k

= 1.3806505(24) × 10⁻²³ J K⁻¹ is Boltzmann's Constant , and the Logarithm is taken to the natural base

e

W

is the number of possible Microstates corresponding to the Macroscopic state of a system — the number of (unobservable) "ways" the (observable) Thermodynamic state of a system can be realized by assigning different Positions and Momenta to the various molecules. Boltzmann’s Paradigm was an Ideal Gas of

N

''identical'' particles, of which

N_i

are in the

i

-th microscopic condition (range) of position and momentum.

W

can be counted using the formula for Permutations

:

W = N!\; / \; \prod_i N_i!

where ''i'' ranges over all possible molecular conditions. (

!

denotes Factorial .) The "correction" in the denominator is due to the fact that identical particles in the same condition are Indistinguishable .

W

is called the " Thermodynamic Probability " since it is an Integer greater than one, while Mathematical Probabilities are always Number s between zero and one.

The equation for

S

is engraved on Boltzmann's Tombstone at the Vienna Zentralfriedhof — his second grave.

THE BOLTZMANN EQUATION

.]]
See Also: Boltzmann equation

The Boltzmann equation was developed to describe the dynamics of an Ideal Gas .

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Ludwig Boltzmann