|
|
| Line 1: |
Line 1: |
| {{distinguish|Stefan–Boltzmann constant}}
| | You might be thinking it's impossible to grow taller because you are short because of your gene. Any time you install or adjust an antenna, perform a channel scan with your digital converter to see if you have improved reception and perhaps more channels available to you. During the day, your spine gets pulled downward a lot when you are standing, so it is good to counteract this at night. Do you wish you ended up a tiny taller than you are now. Most importantly, you will need the terrarium itself. <br><br>As you perform height gain exercises, maintain an effective breathing technique. However, when coupled with the high temperatures you can quickly end up with dried out hard pan if the lawn bed is exposed to direct sunlight. Athletes from an array of sports use plyometric training to help them reach peak of plyometrics sessions along with a variety of upper and lower body mated drills. There are a number of factors that will help determine how tall someone can grow to become. This subconscious mind of yours even control and influence the functions of your body even when you sleep such as your breathing, heart beat, digestion system etc. <br><br>If that bit just described you, then you are in luck. If this is not you, chances are you still could use some work. These cells are equipped with receptors that receive the chemicals being released by the brain and respond to them accordingly. Apart from exercises to grow taller, a proper diet as well plays a great role in the growth of anyone. You want to keep your insulin levels in check, and this will help you to do that. <br><br>The way you do this, is by moving the bicycle seat up a few inches, making it a bit higher than it was. The functions of your body will be accelerated so that what works will work better than before. So if you are not able to see over the steering wheel while driving your car or you are being a joke among the taller crowd of your office, start your quest for increasing height and regain your confidence. So never replace your green leafy with fries and chips or you might regret in the end. Drinking plenty of water is also very important if you are on your way to increasing your height. <br><br>These exercises, and other tips, tricks and lessons, are employed by Over 194,00zero people in 174 countries. There are various herbal supplements which are very much helpful and effective in growing taller. This will get the favored rewards for just how long one's bones mature they generate the individual taller. For satisfactory result, try to do yoga as per the guidance of an expert. Try to switch yourself over to a diet that consists of plenty of meat and dairy products, like cheese, yogurt and milk.<br><br>If you beloved this article so you would like to get more info pertaining to how to get taller in a week - [http://www.estampas.info/sitemap/ estampas.info] - kindly visit our own web site. |
| {{Use dmy dates|date=June 2013}}
| |
| | |
| {| class="wikitable" style="float: right;"
| |
| ! Values of ''k''<sub>B</sub><ref name="2010 CODATA">P.J. Mohr, B.N. Taylor, and D.B. Newell (2011), "The 2010 CODATA Recommended Values of the Fundamental Physical Constants" (Web Version 6.0). This database was developed by J. Baker, M. Douma, and S. Kotochigova. Available: http://physics.nist.gov/constants [Thursday, 02-Jun-2011 21:00:12 EDT]. National Institute of Standards and Technology, Gaithersburg, MD 20899.</ref>
| |
| ! Units
| |
| |-
| |
| | {{gaps|1.3806488(13)}}{{e|−23}} || [[joule|J]] [[kelvin|K]]<sup>−1</sup>
| |
| |-
| |
| | {{gaps|8.6173324(78)}}{{e|-5}} || [[electron-volt|eV]] K<sup>−1</sup>
| |
| |-
| |
| | {{gaps|1.3806488(13)}}{{e|−16}} || [[erg]] K<sup>−1</sup>
| |
| |-
| |
| | colspan=2 | <small>For details, see [[Boltzmann constant#Value in different units|Value in different units]] below.</small>
| |
| |}
| |
| | |
| The '''Boltzmann constant''' (''k''<sub>B</sub> or ''k''), named after [[Ludwig Boltzmann]], is a [[physical constant]] relating [[energy]] at the individual [[particle]] level with [[temperature]]. It is the [[gas constant]] ''R'' divided by the [[Avogadro constant]] ''N''<sub>A</sub>:
| |
| | |
| :<math> k_\mathrm{B} = \frac{R}{N_{\rm A}}.\,</math>
| |
| | |
| It has the same [[Dimensional analysis|dimension]] ([[energy]] divided by [[temperature]]) as [[entropy]].
| |
| | |
| ==Bridge from macroscopic to microscopic physics==
| |
| Boltzmann's constant, ''k''<sub>B</sub>, is a bridge between [[Macroscopic scale|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]] ''n'' (in [[mole (unit)|moles]]) and [[absolute temperature]] ''T'':
| |
| | |
| :<math>PV = nRT \,</math>
| |
| | |
| where ''R'' is the [[gas constant]] ({{nowrap|8.314 4621(75) J K<sup>−1</sup> mol<sup>−1</sup>}}<ref name="2010 CODATA" />). Introducing the Boltzmann constant transforms the ideal gas law into an alternative form:
| |
| :<math>P V = N k_\mathrm{B} T \,</math>
| |
| where ''N'' is the [[Number of particles|number of molecules]] of gas. For ''n'' = 1 [[Mole (unit)|mol]], ''N'' is equal to the number of particles in one mole ([[Avogadro's number]]).
| |
| | |
| The left-hand side of the equation is a macroscopic amount of pressure-volume energy representing the state of the bulk gas. The right-hand side divides this energy into ''N'' units, one for each gas particle, each of which has an average kinetic energy equal to ''k''<sub>B</sub>.
| |
| | |
| ==Role in the equipartition of energy==
| |
| {{main|Equipartition of energy}}
| |
| Given a [[thermodynamics|thermodynamic]] system at an [[thermodynamic temperature|absolute temperature]] ''T'', the thermal energy carried by each microscopic "degree of freedom" in the system is on the [[order of magnitude]] of ''k<sub>B</sub>T''/2 (''i. e.,'' about 2.07{{e|−21}} J, or 0.013 [[electron volt|eV]], at room temperature).
| |
| | |
| ===Application to simple gas thermodynamics===
| |
| In [[classical mechanics|classical]] [[statistical mechanics]], this average is predicted to hold exactly for homogeneous [[ideal gas]]es. Monatomic ideal gases possess three [[degrees of freedom (physics and chemistry)|degrees of freedom]] per atom, corresponding to the three spatial directions, which means a thermal energy of 1.5''k''<sub>B</sub> per atom (in the general case, ''Dk<sub>B</sub>T/2'', where D is the number of spatial dimensions). 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]].
| |
| | |
| [[Kinetic theory#Pressure|Kinetic theory]] gives the average pressure ''p'' for an ideal gas as
| |
| :<math> P = \frac{1}{3}\frac{N}{V} m \overline{v^2}.</math>
| |
| Substituting that the average translational kinetic energy is
| |
| :<math> \tfrac{1}{2}m \overline{v^2} = \tfrac{3}{2} k_\mathrm{B} T</math>
| |
| gives
| |
| :<math> P = \frac{N k_\mathrm{B} T}{V}</math>
| |
| so the ideal gas equation is regained.
| |
| | |
| The ideal gas equation is also obeyed closely by molecular gases; but the form for the heat capacity is more complicated, because the molecules possess additional 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 a total of six degrees of simple freedom per molecule that are related to atomic motion (three translational, two rotational, and one vibrational). At lower temperatures, not all these degrees of freedom may fully participate in the gas heat capacity, due to quantum mechanical limits on the availability of excited states, at the thermal energy available.
| |
| | |
| ==Role in Boltzmann factors==
| |
| More generally, systems in equilibrium at temperature ''T'' have probability ''p'' of occupying a state ''i'' with energy ''E'' weighted by the corresponding [[Boltzmann factor]]:
| |
| :<math>p_i \propto \frac{\exp\left(-\frac{E}{k_\mathrm{B} T}\right)}{Z},\ </math>
| |
| where Z is the [[Partition function (statistical mechanics)|partition function]].
| |
| Again, it is the energy-like quantity [[kT_(energy)|''k''<sub>B</sub>]] which takes central importance.
| |
| | |
| Consequences of this include (in addition to the results for ideal gases above) the [[Arrhenius equation]] in [[chemical kinetics]].
| |
| | |
| ==Role in the statistical definition of entropy==
| |
| <!-- [[Dimensionless entropy]] redirects here -->
| |
| {{further2|[[Entropy (statistical thermodynamics)]]}}
| |
| [[Image:Zentralfriedhof Vienna - Boltzmann.JPG|thumb|right|200px|Boltzmann's grave in the [[Zentralfriedhof]], Vienna, with bust and entropy formula.]]
| |
| In statistical mechanics, the [[entropy]] ''S'' of an [[isolated system]] at [[thermodynamic equilibrium]] is defined as the [[natural logarithm]] of ''W'', the number of distinct microscopic states available to the system given the macroscopic constraints (such as a fixed total energy ''E''):
| |
| :<math>S = k_\mathrm{B}\,\ln W.</math>
| |
| | |
| This equation, which relates the microscopic details, or microstates, of the system (via ''W'') 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.
| |
| | |
| The constant of proportionality ''k''<sub>B</sub> serves to make the statistical mechanical entropy equal to the classical thermodynamic entropy of Clausius:
| |
| :<math>\Delta S = \int \frac{{\rm d}Q}{T}.</math>
| |
| | |
| One could choose instead a rescaled [[dimensionless]] entropy in microscopic terms such that
| |
| | |
| :<math>{S' = \ln W} \; ; \; \; \; \Delta S' = \int \frac{\mathrm{d}Q}{k_\mathrm{B} T}.</math>
| |
| | |
| This is a rather more natural form; and this rescaled entropy exactly corresponds to Shannon's subsequent [[information entropy]].
| |
| | |
| The characteristic energy ''k''<sub>B</sub> is thus the heat required to increase the rescaled entropy by one [[nat (information)|nat]].
| |
| | |
| ==Role in semiconductor physics: the thermal voltage==
| |
| <!-- This section is linked from [[Bipolar junction transistor]] -->
| |
| 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 ''V''<sub>''T''</sub>. The thermal voltage depends on absolute temperature ''T'' as
| |
| :<math> V_T = { k_\mathrm{B}T \over q },</math>
| |
| where ''q'' is the magnitude of the [[elementary charge|electrical charge on the electron]] with a value {{nowrap|1.602 176 565(35){{e|−19}} [[Coulomb|C]]}}<ref name="2010 CODATA" /> and k is the [[Boltzmann's constant]], 1.3806488(13) × 10<sup>−23</sup> J/K. In [[electronvolt]]s, the Boltzmann constant is {{nowrap|8.617 3324(78){{e|−5}} eV/K}},<ref name="2010 CODATA" /> making it easy to calculate that at [[room temperature]] (≈ 300 K), the value of the thermal voltage is approximately 25.85 millivolts ≈ 26 mV.<ref>[http://www.google.com/search?hl=en&q=300+kelvin+*+k+%2F+elementary+charge+in+millivolts 300 kelvin * k / elementary charge in millivolts - Google Search<!-- Bot generated title -->]</ref> The thermal voltage is also important in plasmas and electrolyte solutions; in both cases it provides a measure of how much the spatial distribution of electrons or ions is affected by a boundary held at a fixed voltage.<ref name=Kirby>{{Citation | author=Kirby BJ. | title=Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices |
| |
| url=http://www.kirbyresearch.com/textbook}}</ref><ref name=Tabeling>{{Citation | author=Tabeling | title=Introduction to Microfluidics |
| |
| year=2006}}</ref>
| |
| | |
| ==History==
| |
| 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''<sub>B</sub>, and gave an accurate value for it (1.346{{e|−23}} J/K, about 2.5% lower than today's figure), in his derivation of the [[Planck's law|law of black body radiation]] in 1900–1901.<ref name="Planck01">{{citation | first = Max | last = Planck | author-link = Max Planck | title = Ueber das Gesetz der Energieverteilung im Normalspectrum | url = http://www.physik.uni-augsburg.de/annalen/history/historic-papers/1901_309_553-563.pdf | journal = [[Annalen der Physik|Ann. Phys.]] | year = 1901 | volume = 309 | issue = 3 | pages = 553–63 | doi = 10.1002/andp.19013090310|bibcode = 1901AnP...309..553P }}. English translation: "[http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html On the Law of Distribution of Energy in the Normal Spectrum]{{dead link|date=December 2013}}".</ref> Before 1900, equations involving Boltzmann factors were not written using the energies per molecule and the Boltzmann constant, but rather using a form of the [[gas constant]] ''R'', and macroscopic energies for macroscopic quantities of the substance. The iconic terse form of the equation ''S'' = ''k''<sub>B</sub> log ''W'' on Boltzmann's tombstone is in fact due to Planck, not Boltzmann. Planck actually introduced it in the same work as his ''h''.<ref>{{cite journal |first=Bertrand |last=Duplantier |title=Le mouvement brownien, 'divers et ondoyant' |language=French |trans_title=Brownian motion, 'diverse and undulating' |url=http://www.bourbaphy.fr/duplantier2.pdf |format=PDF |journal=Séminaire Poincaré 1 |pages=155–212 |year=2005}}</ref>
| |
| | |
| As Planck wrote in his [[Nobel Prize]] lecture in 1920,<ref name="PlanckNobel">{{citation | first = Max | last = Planck | author-link = Max Planck | title = The Genesis and Present State of Development of the Quantum Theory (Nobel Lecture) | url = http://nobelprize.org/nobel_prizes/physics/laureates/1918/planck-lecture.html | date = 2 June 1920}}</ref>
| |
| {{quotation|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.}}
| |
| | |
| This "peculiar state of affairs" can be understood by reference to one of the great scientific debates of the time. There was considerable disagreement in the second half of the nineteenth century as to whether atoms and molecules were "real" or whether they were simply a [[heuristic]], a useful tool for solving problems. Nor was there agreement as to whether "chemical molecules" (as measured by [[atomic weight]]s) were the same as "physical molecules" (as measured by [[kinetic theory]]). To continue the quotation from Planck's 1920 lecture:<ref name="PlanckNobel" />
| |
| {{quotation|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.}}
| |
| | |
| In 2013 the UK [[National Physical Laboratory]] used microwave and acoustic resonance measurements to determine the speed of sound of a monatomic gas in a triaxial ellipsoid chamber to determine a more accurate value for the constant as a part of the revision of the [[International System of Units]]. The new value was calculated as 1.380 651 56 (98) × 10<sup>−23</sup> J K<sup>−1</sup> and is expected to be accepted by the [[International System of Units]] following a review.<ref>{{cite DOI|10.1088/0026-1394/50/4/354}}</ref>
| |
| | |
| ==Value in different units==
| |
| {{See also|New SI definitions}}
| |
| {| class="wikitable"
| |
| |-
| |
| ! Values of ''k''<sub>B</sub>
| |
| ! Units
| |
| ! Comments
| |
| |-
| |
| | 1.380 6488(13){{e|−23}} || [[joule|J]]/[[kelvin|K]] || [[SI]] units, 2010 [[CODATA]] value, J/K = m<sup>2</sup>·kg/(s<sup>2</sup>·K) in SI base units<ref name="2010 CODATA" />
| |
| |-
| |
| | 8.617 3324(78){{e|−5}} || [[electronvolt|eV]]/K || 2010 [[CODATA]] value<ref name="2010 CODATA" /><br /><!--
| |
| -->1 [[electronvolt]] = [[1 E-19 J|1.602 176 565(35){{e|−19}}]] J<ref name="2010 CODATA" />
| |
| 1/''k''<sub>B</sub> = 11 604.519(11) K/eV
| |
| |-
| |
| | 2.083 6618(19){{e|10}} || [[Hertz|Hz]]/K || 2010 [[CODATA]] value<ref name="2010 CODATA" /><br /><!--
| |
| -->1 Hz·[[Planck's constant|''h'']] = 6.626 069 57(29){{e|−34}} J<ref name="2010 CODATA" />
| |
| |-
| |
| | 3.166 8114(29){{e|−6}} || [[Hartree|''E''<sub>H</sub>]]/K || ''E''<sub>H</sub> = 2[[Rydberg constant|''R''<sub>∞</sub>]]''hc'' = 4.359 744 34(19){{e|−18}} J<ref name="2010 CODATA" /><br /><!--
| |
| --> = 6.579 683 920 729(33) Hz·''h''<ref name="2010 CODATA" />
| |
| |-
| |
| | 1.380 6488(13){{e|−16}} || [[erg]]/K || [[Centimetre–gram–second system of units|CGS]] system, 1 [[erg]] = 1{{e|−7}} J
| |
| |-
| |
| | 3.297 6230(30){{e|−24}} || [[Calorie|cal]]/K || 1 [[Steam table]] [[calorie]] = 4.1868 J
| |
| |-
| |
| | 1.832 0128(17){{e|−24}} || cal/[[Rankine scale|°R]] || 1 [[Rankine scale|degree Rankine]] = 5/9 K
| |
| |-
| |
| | 5.657 3016(51){{e|−24}} || [[Foot-pound force|ft lb]]/°R || 1 [[foot-pound force]] = 1.355 817 948 331 4004 J
| |
| |-
| |
| | 0.695 034 76(63) || [[Wavenumber|cm<sup>−1</sup>]]/K || 2010 [[CODATA]] value<ref name="2010 CODATA" /><br /><!--
| |
| -->1 cm<sup>−1 </sup>·''hc'' = 1.986 445 683(87){{e|−23}} J
| |
| |-
| |
| | 0.001 987 2041(18) || kcal/[[mole (unit)|mol]]/K || per mole form often used in statistical mechanics—using thermochemical calorie = 4.184 Joule
| |
| |-
| |
| | 0.008 314 4621(75) || kJ/mol/K || per mole form often used in statistical mechanics
| |
| |-
| |
| | 4.10 || pN·nm || ''k''<sub>B</sub> in piconewton nanometer at 24°C, used in biophysics
| |
| |-
| |
| | −228.599 1678(40) || dBW/K/Hz || in [[decibel watt]]s, used in telecommunications (see [[Johnson–Nyquist noise]])
| |
| |-
| |
| | 1.442 695 041... || [[bit]] || in bits (logarithm base 2), used in [[information entropy]] (exact value 1/ln(2))
| |
| |-
| |
| | 1 || [[Nat (information)|nat]] || in nats (logarithm base e), used in [[information entropy]] (see Planck Units, below)
| |
| |}
| |
| | |
| Since ''k''<sub>B</sub> is a [[physical constant]] of proportionality between temperature and energy, its numerical value depends on the choice of units for energy and temperature. The small numerical value of the Boltzmann constant in [[SI]] units reflects the small energy in Joule required to increase a particle's energy by raising the temperature by [[Kelvin|1 K]]. [[Celsius|1 °C]] is defined to be the same as 1 K. The characteristic energy ''k''<sub>B</sub> is a term encountered in many physical relationships.
| |
| | |
| ===Planck units===
| |
| The Boltzmann constant provides a mapping from this characteristic microscopic energy ''E'' to the macroscopic temperature scale ''T'' = ''E''/''k''<sub>B</sub>. In physics research another definition is often encountered in setting ''k''<sub>B</sub> to unity, resulting in the Planck units or [[natural units]] for temperature and energy. In this context temperature is measured effectively in units of energy and the Boltzmann constant is not explicitly needed.<ref>{{citation | doi = 10.1007/s11018-005-0195-9 | author = Kalinin, M; Kononogov, S | title = Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility | journal = Measurement Techniques | pages = 632–36 | volume = 48 | issue = 7 | year = 2005}}</ref>
| |
| :<math>E = \frac{1}{2} T \ </math>
| |
| This simplifies many physical relationships and makes the definition of thermodynamic entropy coincide with that of [[information entropy]]:
| |
| :<math> S = - \sum P_i \ln P_i.</math>
| |
| where ''P''<sub>i</sub> is the probability of each [[Microstate (statistical mechanics)|microstate]].
| |
| | |
| The value chosen for a unit of the [[Planck temperature]] is that corresponding to the energy of the [[Planck mass]] or {{nowrap|[[1 E30 K|1.416 833(85){{e|32}} K]]}}.<ref name="2010 CODATA" />
| |
| | |
| ==References==
| |
| {{Reflist}}
| |
| | |
| ==External links==
| |
| *[http://www.bipm.org/utils/common/pdf/si_brochure_draft_ch2.pdf Draft Chapter 2 for SI Brochure, following redefinitions of the base units] (prepared by the Consultative Committee for Units)
| |
| *[http://www.sciencedaily.com/releases/2011/09/110920075520.htm Big Step Towards Redefining the Kelvin: Scientists Find New Way to Determine Boltzmann Constant]
| |
| | |
| {{DEFAULTSORT:Boltzmann Constant}}
| |
| [[Category:Statistical mechanics]]
| |
| [[Category:Thermodynamics]]
| |
| [[Category:Fundamental constants]]
| |
| [[Category:Physical constants]]
| |
You might be thinking it's impossible to grow taller because you are short because of your gene. Any time you install or adjust an antenna, perform a channel scan with your digital converter to see if you have improved reception and perhaps more channels available to you. During the day, your spine gets pulled downward a lot when you are standing, so it is good to counteract this at night. Do you wish you ended up a tiny taller than you are now. Most importantly, you will need the terrarium itself.
As you perform height gain exercises, maintain an effective breathing technique. However, when coupled with the high temperatures you can quickly end up with dried out hard pan if the lawn bed is exposed to direct sunlight. Athletes from an array of sports use plyometric training to help them reach peak of plyometrics sessions along with a variety of upper and lower body mated drills. There are a number of factors that will help determine how tall someone can grow to become. This subconscious mind of yours even control and influence the functions of your body even when you sleep such as your breathing, heart beat, digestion system etc.
If that bit just described you, then you are in luck. If this is not you, chances are you still could use some work. These cells are equipped with receptors that receive the chemicals being released by the brain and respond to them accordingly. Apart from exercises to grow taller, a proper diet as well plays a great role in the growth of anyone. You want to keep your insulin levels in check, and this will help you to do that.
The way you do this, is by moving the bicycle seat up a few inches, making it a bit higher than it was. The functions of your body will be accelerated so that what works will work better than before. So if you are not able to see over the steering wheel while driving your car or you are being a joke among the taller crowd of your office, start your quest for increasing height and regain your confidence. So never replace your green leafy with fries and chips or you might regret in the end. Drinking plenty of water is also very important if you are on your way to increasing your height.
These exercises, and other tips, tricks and lessons, are employed by Over 194,00zero people in 174 countries. There are various herbal supplements which are very much helpful and effective in growing taller. This will get the favored rewards for just how long one's bones mature they generate the individual taller. For satisfactory result, try to do yoga as per the guidance of an expert. Try to switch yourself over to a diet that consists of plenty of meat and dairy products, like cheese, yogurt and milk.
If you beloved this article so you would like to get more info pertaining to how to get taller in a week - estampas.info - kindly visit our own web site.