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The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. The joule (IPA: or ) (symbol: J) is the SI unit of energy. ...
For other uses, see Kelvin (disambiguation). ...
An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...
An erg is the unit of energy and mechanical work in the centimetre-gram-second (CGS) system of units, symbol erg. Its name is derived from the Greek word meaning work. The erg is a small unit, equal to a force of one dyne exerted for a distance of one...
In physics, a physical constant is a physical quantity of a value that is generally believed to be both universal in nature and not believed to change in time. ...
For other uses, see Temperature (disambiguation). ...
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. Ludwig Eduard Boltzmann (Vienna, Austrian Empire, February 20, 1844 – Duino near Trieste, September 5, 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. ...
Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...
Bridge from macroscopic to microscopic physics
Boltzmann's constant k is a bridge between macroscopic and microscopic physics. Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure p and volume V is proportional to the product of amount of substance and absolute temperature. Macroscopic is commonly used to describe physical objects that are measurable and observable by the naked eye. ...
Isotherms of an ideal gas The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834. ...
An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ...
This article is about pressure in the physical sciences. ...
The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ...
The amount of substance, n, of a sample or system is a physical quantity which is proportional to the number of elementary entities present. ...
Absolute zero is the lowest temperature that can be obtained in any macroscopic system. ...
 where  is called the gas constant [8.314 472 m3·Pa·K−1·mol−1], Introducing Boltzmann's constant transforms this into an equation about the microscopic properties of molecules, The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ...
 where N is the number of molecules of gas, and k is Boltzmann's constant.
Role in the equipartition of energy Given a thermodynamic system at an absolute temperature T, the thermal energy carried by each microscopic "degree of freedom" in the system is on the order of magnitude of kT/2 (i.e., about 2.07×10−21 J, or 0.013 eV at room temperature). Thermodynamics (from the Greek θεÏμη, therme, meaning heat and δυναμις, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ...
Absolute zero is the lowest possible temperature where nothing could be colder, and no heat energy remains in a substance. ...
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ...
An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...
Application to simple gas thermodynamics In 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 1.5kT per atom. As indicated in the article on heat capacity, this corresponds very well with experimental data. The thermal energy can be used to calculate the root mean square speed of the atoms, which is inversely proportional to the square root of the atomic mass. The root mean square speeds found at room temperature accurately reflect this, ranging from 1370 m/s for helium, down to 240 m/s for xenon. Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ...
Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...
An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ...
The atomic mass (ma) is the mass of an atom at rest, most often expressed in unified atomic mass units. ...
For other uses, see Helium (disambiguation). ...
General Name, Symbol, Number xenon, Xe, 54 Chemical series noble gases Group, Period, Block 18, 5, p Appearance colorless Standard atomic weight 131. ...
Kinetic theory gives the average pressure p for an ideal gas as Kinetic theory or kinetic theory of gases attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. ...
 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 factors More generally, systems in equilibrium with a reservoir of heat at temperature T have probabilities of occupying states with energy E weighted by the corresponding Boltzmann factor: In physics, the Boltzmann factor is a weighting factor determining the relative probability of a system in thermodynamic equilibrium at a temperature T being in a state with energy E: (kB is Boltzmanns constant. ...
 Again, it is the energy-like quantity kT which takes central importance.
Consequences of this include (in addition to the results for ideal gases above), for example the Arrhenius equation of simple chemical kinetics. The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of a chemical reaction rate, more correctly, of a rate coefficient, as this coefficient includes all magnitudes that affect reaction rate except for concentration. ...
Role in definition of entropy -
Main article: Boltzmann's entropy formula In statistical mechanics, the entropy S of an isolated system at thermodynamic equilibrium is defined as the natural logarithm of Ω, the number of distinct microscopic states available to the system given the macroscopic constraints (such as a fixed total energy E): Boltzmanns equation - carved in stone. ...
For a less technical and generally accessible introduction to the topic, see Introduction to entropy. ...
Isolation can refer to: Isolation as a psychological phenomenon. ...
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ...
The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is an irrational constant approximately equal to 2. ...
 This equation, which relates the microscopic details of the system (via Ω) to its macroscopic state (via the entropy S), is the central idea of statistical mechanics. Such is its importance that it is inscribed on Boltzmann's tombstone. Ludwig Boltzmann Ludwig Boltzmann (February 20, 1844 – September 5, Austrian physicist famous for the invention of statistical mechanics. ...
The constant of proportionality k appears in order to make the statistical mechanical entropy equal to the classical thermodynamic entropy of Clausius:
 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. Claude Shannon In information theory, the Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable. ...
Role in semiconductor physics: The Thermal Voltage In 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 thermal voltage, denoted VT. The thermal voltage depends on absolute temperature T (in kelvins) as A semiconductor is a material that is an insulator at very low temperature, but which has a sizable electrical conductivity at room temperature. ...
In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ...
Electric potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. ...
A p-n junction is formed by combining N-type and P-type semiconductors together in very close contact. ...
 where q is the magnitude of the electrical charge (in coulombs) on the electron. At room temperature (T ≈ 300 K), the value of the thermal voltage is approximately 26 millivolts. See also semiconductor diodes. Closeup of the image below, showing the square shaped semiconductor crystal various semiconductor diodes, below a bridge rectifier Structure of a vacuum tube diode In electronics, a diode is a component that restricts the directional flow of charge carriers. ...
Boltzmann's constant in Planck units Planck's system of natural units is one system constructed such that the Boltzmann constant is 1. This gives In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. ...
 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 1.41679×1032 K. The Planck temperature, named after German physicist Max Planck, is the natural unit of temperature, denoted by TP. The Planck units, in general, represent limits of quantum mechanics. ...
The Planck mass is the natural unit of mass, denoted by mP. It is the mass for which the Schwarzschild radius is equal to the Compton length divided by π. ≈ 1. ...
To help compare different orders of magnitude this page lists temperatures above 1030 kelvins. ...
Historical Note Although Boltzmann first linked entropy and probability in 1877, it seems the relation was never expressed with a specific constant until Max Planck first introduced k , and gave an accurate value for it, in his derivation of the law of black body radiation in December 1900. The iconic terse form of the equation S = k log W on Boltzmann's tombstone is in fact due to Planck, not Boltzmann. 1877 (MDCCCLXXVII) was a common year starting on Monday (see link for calendar). ...
“Planck†redirects here. ...
Black body spectrum In physics, Plancks law of black body radiation predicts the spectral intensity of electromagnetic radiation at all wavelengths from a black body at temperature : where the following table provides the definition and SI units of measure for each symbol: The wavelength is related to the frequency...
As Planck wrote in his 1918 Nobel Prize lecture, The Nobel Prizes (Swedish: ) are awarded for Physics, Chemistry, Literature, Peace, and Physiology or Medicine. ...
- "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 R, and macroscopic energies for macroscopic quantities of the substance; as for convenience is still generally the case in Chemistry to this day. The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ...
Value in different units | Values of k | Units | Comments | | 1.380 6504(24)×10−23 | J/K | SI units, 2002 CODATA value | | 8.617 343(15)×10−5 | eV/K | 1 electronvolt = 1.602 176 53(14)×10−19 J | | 1.3807×10−16 | erg/K | The digits in parentheses are the standard measurement uncertainty in the last two digits of the measured value. The joule (IPA: or ) (symbol: J) is the SI unit of energy. ...
For other uses, see Kelvin (disambiguation). ...
Look up si, Si, SI in Wiktionary, the free dictionary. ...
CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ...
An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...
The electronvolt (symbol eV) is a unit of energy. ...
To help compare different orders of magnitude we list here energies between 10−19 joules and 10−18 joules (0. ...
An erg is the unit of energy and mechanical work in the centimetre-gram-second (CGS) system of units, symbol erg. Its name is derived from the Greek word meaning work. The erg is a small unit, equal to a force of one dyne exerted for a distance of one...
The measurement uncertainty quantifies the distance between the actually measured value of a physical quantity and the true value of the same physical quantity. ...
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. MOL can refer to: Manned Orbiting Laboratory Method of Levels (psychotherapy) MOL, (Hungarian Oil and Gas Public Limited Company [1]) Method of Lines Mac-on-Linux, a software environment for PowerPC Linux which can run Mac OS (or Mac OS X) and its applications This page concerning a three-letter...
The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ...
The numerical value of k has no particular fundamental significance in itself: It merely reflects a preference for measuring temperature in units of familiar kelvins, based on the macroscopic physical properties of water. What is physically fundamental is the characteristic energy kT at a particular temperature. The numerical value of k measures the conversion factor for mapping from this characteristic microscopic energy E to the macroscopically-derived temperature scale T = E/k . If, instead of talking of room temperature as 300 K (27 °C or 80 °F), it were conventional to speak of the corresponding energy kT of 4.14×10−21 J, or 0.0259 eV, then Boltzmann's constant would not be needed. For other uses, see Kelvin (disambiguation). ...
For other uses, see Room temperature (disambiguation). ...
Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ...
For other uses, see Fahrenheit (disambiguation). ...
An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...
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
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