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## Boltzmann constant
The It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this constant plays a crucial role.
## Bridge from macroscopic to microscopic physicsBoltzmann's constant p and volume V is proportional to the product of amount of substance n (in number of moles) and absolute temperature T.
where - is called the gas constant [8.314 472 m
^{3}·Pa·K^{−1}·mol^{−1}],
Introducing Boltzmann's constant transforms this into an equation about the where is Boltzmann's constant.
k## Role in the equipartition of energyGiven a thermodynamic system at an absolute temperature ## Application to simple gas thermodynamicsIn classical statistical mechanics, this average is predicted to hold exactly for homogeneous ideal gases. Monatomic ideal gases possess 3 degrees of freedom per atom, corresponding to the three spatial directions, which means a thermal energy of Kinetic theory gives the average pressure Substituting that the average translational kinetic energy is and gives so the ideal gas equation is regained. The ideal gas equation is also followed quite well for molecular gases; but the form for the heat capacity is more complicated, because the molecules possess new internal degrees of freedom, as well as the three degrees of freedom for movement of the molecule as a whole. Diatomic gases, for example, possess in total approximately 5 degrees of freedom per molecule. ## Role in Boltzmann factorsMore generally, systems in equilibrium with a reservoir of heat at temperature Again, it is the energy-like quantity Consequences of this include (in addition to the results for ideal gases above), for example the Arrhenius equation of simple chemical kinetics. ## Role in definition of entropyIn statistical mechanics, the entropy This equation, which relates the microscopic details of the system (via Ω) to its macroscopic state (via the entropy The constant of proportionality One could choose instead a rescaled entropy in microscopic terms such that This is a rather more natural form; and this rescaled entropy exactly corresponds to Shannon's subsequent information entropy, and could thereby have avoided much unnecessary subsequent confusion between the two. ## Role in semiconductor physics: the thermal voltageIn semiconductors, the relationship between the flow of electrical current and the electrostatic potential across a p-n junction depends on a characteristic voltage called the where ## Boltzmann's constant in Planck unitsPlanck's system of natural units is one system constructed such that the Boltzmann constant is 1. This gives as the average kinetic energy of a gas molecule per degree of freedom; and makes the definition of thermodynamic entropy coincide with that of information entropy: The value chosen for the Planck unit of temperature is that corresponding to the energy of the Planck mass—a staggering 1.41679×10 ## Historical noteAlthough Boltzmann first linked entropy and probability in 1877, it seems the relation was never expressed with a specific constant until Max Planck first introduced As Planck wrote in his 1918 Nobel Prize lecture, - "This constant is often referred to as Boltzmann's constant, although, to my knowledge, Boltzmann himself never introduced it — a peculiar state of affairs, which can be explained by the fact that Boltzmann, as appears from his occasional utterances, never gave thought to the possibility of carrying out an exact measurement of the constant. Nothing can better illustrate the positive and hectic pace of progress which the art of experimenters has made over the past twenty years, than the fact that since that time, not only one, but a great number of methods have been discovered for measuring the mass of a molecule with practically the same accuracy as that attained for a planet." [1]
Before 1900, equations involving Boltzmann factors were not written using the energies per molecule and Boltzmann's constant, but rather using the gas constant ## Value in different units
The digits in parentheses are the standard measurement uncertainty in the last two digits of the measured value. k can also be expressed with the unit mol (such as 1.99 calories/mole-kelvin), for historical reasons it is then called gas constant. The ## References- Boltzmann's constant CODATA value at NIST
- Peter J. Mohr, and Barry N. Taylor, "CODATA recommended values of the fundamental physical constants: 1998", Rev. Mod. Phys., Vol 72, No. 2, April 2000
Categories: Statistical mechanics | Thermodynamics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Boltzmann_constant". A list of authors is available in Wikipedia. |