The Boltzmann constant (k or k_B) is the %20%20%20In%20science%2C%20a%20physical%20constant%20is%20a%20physical%20quantity%20whose%20numerical%20value%20does%20not%20change.%20... physical constant relating %20%20%20Temperature%20is%20the%20physical%20property%20of%20a%20system%20which%20underlies%20the%20common%20notions%20of%20%5Chot%5C%20and%20%5Ccold%5C%3B%20the%20material%20with%20the%20higher%20temperature%20is%20said%20to%20be%20hotter.%20%20%20... temperature to %20%20%20Energy%20is%20a%20fundamental%20quantity%20that%20every%20%20%20physical%20%20%20system%20possesses%3B%20it%20allows%20us%20to%20predict%20how%20much%20%20%20work%20the%20system%20could%20be%20made%20to%20do%2C%20or%20how%20much%20%20%20heat%20it%20can%20exchange.%20... energy. It is named after the %20%20%20The%20Republic%20of%20Austria%20(%20%20German%3A%20Republik%20%26%23214%3Bsterreich)%20is%20a%20%20%20landlocked%20country%20in%20%20%20Central%20Europe.%20... Austrian physicist %20%20%20%20%20%20%20Ludwig%20Boltzmann%20%20%20Ludwig%20Boltzmann%20(February%2020%2C%201844%20%26%238211%3B%20September%205%2C%201906)%20was%20an%20Austrian%20physicist%20famous%20for%20the%20invention%20of%20statistical%20mechanics.%20... Ludwig Boltzmann, who made important contributions to the theory of %20%20%20Statistical%20mechanics%20is%20the%20application%20of%20statistics%2C%20which%20includes%20mathematical%20tools%20for%20dealing%20with%20large%20populations%2C%20to%20the%20field%20of%20mechanics%2C%20which%20is%20concerned%20with%20the%20motion%20of%20particles%20or%20objects%20when%20subjected%20to%20a%20force.%20... statistical mechanics, in which this constant plays a crucial role. Its %20%20%20From%20Latin%20ex-%20%2B%20-periri%20(akin%20to%20periculum%20attempt).%20... experimentally determined value is (in %20%20%20%20%20%20SI%20(disambiguation).%20%20... SI units, 2002 %20%20%20CODATA%20(Committee%20on%20Data%20for%20Science%20and%20Technology)%20was%20established%20in%201966%20as%20an%20interdisciplinary%20committee%20of%20the%20International%20Council%20of%20Science%20(ICSU)%2C%20formerly%20the%20International%20Council%20of%20Scientific%20Unions.%20... CODATA value)

k = 1.380 6505(24) × 10⁻²³ %20%20%20The%20joule%20(symbol%20J%2C%20also%20called%20newton%20metre%2C%20or%20coulomb%20volt)%20is%20the%20SI%20unit%20of%20energy%20and%20work.%20... J/%20%20%20%20The%20kelvin%20(symbol%3A%20K)%20is%20the%20SI%20unit%20of%20temperature%2C%20and%20is%20one%20of%20the%20seven%20SI%20base%20units.%20... K.

The digits in parentheses are the uncertainty (%20%20%20In%20probability%20and%20statistics%2C%20the%20standard%20deviation%20is%20the%20most%20commonly%20used%20measure%20of%20statistical%20dispersion.%20... standard deviation) in the last two digits of the measured value. In principle, the Boltzmann constant could be a derived physical constant, as its value is determined by other physical constants and in the definition of unit of absolute %20%20%20Temperature%20is%20the%20physical%20property%20of%20a%20system%20which%20underlies%20the%20common%20notions%20of%20%5Chot%5C%20and%20%5Ccold%5C%3B%20the%20material%20with%20the%20higher%20temperature%20is%20said%20to%20be%20hotter.%20%20%20... temperature. However, calculating the Boltzmann constant from first principles is far too complex to be done with current knowledge. In Planck's system of %20%20In%20physics%2C%20Planck%20units%20are%20physical%20units%20of%20measurement%20originally%20proposed%20by%20Max%20Planck.%20... natural units, the %20%20%20The%20Planck%20temperature%2C%20named%20after%20German%20physicist%20Max%20Planck%2C%20is%20the%20natural%20unit%20of%20temperature%2C%20denoted%20by%20TP.%20... natural unit temperature is such that the Boltzmann constant is one.

The %20%20%20Molar%20gas%20constant%20(also%20known%20as%20universal%20gas%20constant%2C%20usually%20denoted%20by%20symbol%20R)%20is%20the%20constant%20occurring%20in%20the%20universal%20gas%20equation%2C%20i.... universal gas constant R is simply the Boltzmann constant multiplied by Avogadro's number. The gas constant is more useful when calculating numbers of particles in %20%20%20The%20mole%20(symbol%3A%20mol)%20is%20one%20of%20the%20seven%20SI%20base%20units%20and%20is%20commonly%20used%20in%20chemistry.%20... moles.

Role in relating temperature to energy

Given a %20%20%20Thermodynamics%20(Greek%3A%20thermos%20%3D%20heat%20and%20dynamic%20%3D%20change)%20is%20the%20physics%20of%20energy%2C%20heat%2C%20work%2C%20entropy%20and%20the%20spontaneity%20of%20processes.%20... thermodynamic system at an %20%20%20%20%20This%20article%20is%20about%20a%20television%20episode%3B%20for%20the%20temperature%2C%20see%20Absolute%20zero.%20%20%20... absolute temperature T, the thermal energy carried by each microscopic "degree of freedom" in the system is on the %20%20%20%20An%20order%20of%20magnitude%20is%20the%20class%20of%20scale%20or%20magnitude%20of%20any%20amount%2C%20where%20each%20class%20contains%20values%20of%20a%20fixed%20ratio%20to%20the%20class%20preceding%20it.%20... order of magnitude of kT/2. %20%20%20Room%20temperature%2C%20in%20laboratory%20reports%2C%20is%20taken%20to%20be%20roughly%2021%26%238211%3B23%20degrees%20Celsius%20(68%26%238211%3B72%20degrees%20Fahrenheit)%2C%20or%20294%26%238211%3B296%20kelvins.%20... Room temperature, 300 K (27 °%20%20%20%20The%20degree%20Celsius%20(%5CxB0C)%20is%20a%20unit%20of%20temperature%20named%20after%20the%20Swedish%20astronomer%20Anders%20Celsius%20(1701%26%238211%3B1744)%2C%20who%20first%20proposed%20it%20in%201742.%20... C or 80 °%20%20%20%20This%20article%20is%20about%20the%20temperature%20scale%3B%20see%20also%20Fahrenheit%20graphics%20API.%20%20%20... F), corresponds to a kT/2 of 2.07 × 10⁻²¹ J, or 13 %20%20An%20electronvolt%20(symbol%3A%20eV)%20is%20the%20amount%20of%20energy%20gained%20by%20a%20single%20unbound%20electron%20when%20it%20falls%20through%20an%20electrostatic%20potential%20difference%20of%20one%20volt.%20... meV.

In %20%20Classical%20mechanics%20is%20a%20model%20of%20the%20physics%20of%20forces%20acting%20upon%20bodies.%20... classical %20%20%20Statistical%20mechanics%20is%20the%20application%20of%20statistics%2C%20which%20includes%20mathematical%20tools%20for%20dealing%20with%20large%20populations%2C%20to%20the%20field%20of%20mechanics%2C%20which%20is%20concerned%20with%20the%20motion%20of%20particles%20or%20objects%20when%20subjected%20to%20a%20force.%20... statistical mechanics, homogeneous %20%20%20%20An%20ideal%20gas%20(also%20called%20a%20perfect%20gas)%20is%20a%20hypothetical%20fluid%20consisting%20of%20particles%20that%20are%20identical%20to%20each%20other%2C%20occupy%20negligible%20volume%20and%20undergo%20perfect%20elastic%20collisions%20with%20each%20other%2C%20with%20no%20intermolecular%20forces%20and%20no%20intramolecular%20storage%20of%20energy%2C%20as%20opposed%20to%20a%20real%20gas%2C%20a%20gas... ideal gases possess kT/2 per degree of freedom per %20%20%20%20%20%20%20%20%20%20Properties%20%20%20%20%20%20%20%20%20%20%20%20For%20alternative%20meanings%20see%20%20%20atom%20(disambiguation).%20%20... atom. 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 %20%20%20Heat%20capacity%20(abbreviated%20Cth%20or%20just%20C%2C%20also%20called%20thermal%20capacity)%20is%20the%20ability%20of%20matter%20to%20store%20heat.%20... heat capacity, this corresponds very well with experimental data. The thermal energy can be used to calculate the %20%20%20In%20mathematics%2C%20the%20root%20mean%20square%20or%20rms%20is%20a%20statistical%20measure%20of%20the%20magnitude%20of%20a%20varying%20quantity.%20... root mean square speed of the atoms, which is inversely proportional to the square root of the %20%20%20%20%20%20%20%20%20%20... atomic mass. The root mean square speed at room temperature ranges from 1370 m/s for %20%20%20%20%20%20%20General%20%20%20Name%2C%20Symbol%2C%20Number%20Helium%2C%20He%2C%202%20%20%20Atomic%20weight%204.... helium, down to 240 m/s for %20%20%20%20%20%20%20General%20%20%20Name%2C%20Symbol%2C%20Number%20xenon%2C%20Xe%2C%2054%20%20%20Chemical%20series%20Noble%20gases%20%20%20Group%2C%20Period%2C%20Block%2018%20(VIIIA)%2C%205%2C%20p%20%20%20Density%2C%20Hardness%205.... xenon. The situation is more complicated for molecular gases; diatomic gases, for example, possess approximately 5 degrees of freedom per molecule.

Role in definition of entropy

In statistical mechanics, the %20%20%20%20For%20other%20uses%20of%20the%20term%20entropy%2C%20see%20Entropy%20(disambiguation)%20%20The%20thermodynamic%20entropy%20S%2C%20often%20simply%20called%20the%20entropy%20in%20the%20context%20of%20thermodynamics%2C%20is%20a%20measure%20of%20the%20amount%20of%20energy%20in%20a%20physical%20system%20that%20cannot%20be%20used%20to%20do%20work.%20... entropy S of a system is defined as the %20%20%20The%20natural%20logarithm%20is%20the%20logarithm%20to%20the%20base%20e%2C%20where%20e%20is%20approximately%20equal%20to%202.... 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):

The constant of proportionality k is the Boltzmann constant. 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.

Reference

• Boltzmann's constant CODATA value (http://physics.nist.gov/cgi-bin/cuu/Value?eqk|search_for=Boltzmann) at %20%20%20As%20a%20non-regulatory%20agency%20of%20the%20United%20States%20Department%20of%20Commerce%26%238217%3Bs%20Technology%20Administration%2C%20the%20National%20Institute%20of%20Standards%20(NIST)%20develops%20and%20promotes%20measurement%2C%20standards%2C%20and%20technology%20to%20enhance%20productivity%2C%20facilitate%20trade%2C%20and%20improve%20the%20quality%20of%20life.%20... 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