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| | Name: Olive Breeze<br>My age: 20<br>Country: Germany<br>Town: Timmendorfer Strand <br>Post code: 23665<br>Street: Nuernbergerstrasse 9<br><br>Feel free to visit my blog post; [http://www.pelinbaris.com/defter/index.php fifa coin generator] |
| ! Values of ''R''<br /><ref name="CODATA">{{CODATA2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?r}}</ref>
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| ! Units<br />[[Ideal gas law|(V P T<sup> −1</sup> n<sup>−1</sup>)]]
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| |-
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| | {{val|8.3144621|(75)}}<ref name="CODATA10">[http://physics.nist.gov/cgi-bin/cuu/Value?r 2010 CODATA recommended value of R]</ref>
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| | [[Joule|J]] [[Kelvin|K]]<sup>−1</sup> [[Mole (unit)|mol]]<sup>−1</sup>
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| |-
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| | {{val|8.3144621|(75)}}
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| | [[Volt|V]][[Coulomb|C]] [[Kelvin|K]]<sup>−1</sup> [[Mole (unit)|mol]]<sup>−1</sup>
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| |-
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| | {{val|5.189|e=19}}
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| | [[electron Volt|eV]] [[Kelvin|K]]<sup>−1</sup> [[Mole (unit)|mol]]<sup>−1</sup>
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| |-
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| | {{val|0.08205746|(14)}}
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| | [[Liter|L]] [[atmosphere (unit)|atm]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|1.9872041|(18)}}<ref name="IUPACGOLDcalorie">[http://goldbook.iupac.org/C00784.html?Thermochemical calorie 4.184 J should be used (IUPAC Gold Book)]</ref>
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| | [[calorie|cal]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|1.9872041|(18)|e=-3}}
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| | [[kilocalorie|kcal]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|8.3144621|(75)|e=7}}
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| | [[erg]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|8.3144621|(75)|e=-3}}
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| | [[atomic mass unit | amu]] (km/s)<sup>2</sup> K<sup>−1
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| |-
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| | {{val|8.3144621|(75)}}
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| | L [[Pascal (unit)|kPa]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|8.3144621|(75)|e=3}}
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| | [[cubic centimeter|cm<sup>3</sup>]] [[Pascal (unit)|kPa]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|8.3144621|(75)}}
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| | [[cubic metre|m<sup>3</sup>]] [[Pascal (unit)|Pa]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|8.3144621|(75)}}
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| | [[cubic centimeter|cm<sup>3</sup>]] [[Megapascal|MPa]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|8.3144621|(75)|e=-5}}
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| | m<sup>3</sup> [[bar (unit)|bar]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|8.205736|e=-5}}
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| | m<sup>3</sup> [[atm (unit)|atm]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|8.205736|e=-2}}
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| | m<sup>3</sup> [[atm (unit)|atm]] K<sup>−1</sup> kg-mol<sup>−1</sup>
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| |-
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| | {{val|82.05736}}
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| | cm<sup>3</sup> [[atm (unit)|atm]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|84.78402|e=-6}}
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| | m<sup>3</sup> [[Kilogram-force per square centimetre|kgf/cm<sup>2</sup>]] K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|8.3144621|(75)|e=-2}}
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| | L bar K<sup>−1</sup> mol<sup>−1</sup>
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| |-
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| | {{val|62.36367|(11)|e=-3}}
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| | m<sup>3</sup> [[mmHg]] K<sup>−1 </sup> mol<sup>−1</sup>
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| |-
| |
| | {{val|62.36367|(11)}}
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| | L [[mmHg]] K<sup>−1 </sup> mol<sup>−1</sup>
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| |-
| |
| | {{val|62.36367|(11)}}
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| | L [[Torr]] K<sup>−1 </sup> mol<sup>−1</sup>
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| |-
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| | {{val|6.132440|(10)}}
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| | [[foot-pound force|ft lbf]] K<sup>−1</sup> [[mole (unit)|g-mol]]<sup>−1</sup>
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| |-
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| | {{val|1545.34896|(3)}}
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| | ft lbf [[Rankine scale|R]]<sup>−1</sup> [[pound mole|lb-mol]]<sup>−1</sup>
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| |-
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| | {{val|10.73159|(2)}}
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| | [[cubic foot|ft<sup>3</sup>]] [[Pound per square inch|psi]] R<sup>−1</sup> lb-mol<sup>−1</sup>
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| |-
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| | {{val|0.7302413|(12)}}
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| | ft<sup>3</sup> atm R<sup>−1</sup> lb-mol<sup>−1</sup>
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| |-
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| | {{val|1.31443}}
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| | ft<sup>3</sup> atm K<sup>−1</sup> lb-mol<sup>−1</sup>
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| |-
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| | {{val|998.9701|(17)}}
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| | ft<sup>3</sup> mmHg K<sup>−1</sup> lb-mol<sup>−1</sup>
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| |-
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| | {{val|1.986}}
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| | [[British thermal unit|Btu]] lb-mol<sup>−1</sup> R<sup>−1</sup>
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| |-
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| |}
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| The '''gas constant''' (also known as the '''molar''', '''universal''', or '''ideal gas constant''', denoted by the symbol ''R'' or <u style="font-style:italic; text-decoration:overline">R</u>) is a [[physical constant]] which is featured in many fundamental equations in the physical sciences, such as the [[ideal gas law]] and the [[Nernst equation]].
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| It is equivalent to the [[Boltzmann constant]], but expressed in units of [[energy]] (i.e. the pressure-volume product) per [[temperature|temperature increment]] per ''[[mole (unit)|mole]]'' (rather than energy per temperature increment per ''particle''). The constant is also a combination of the constants from [[Boyle's law]], [[Charles's law]], [[Avogadro's law]], and [[Gay-Lussac's law]].
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| Physically, the gas constant is the [[constant of proportionality]] that happens to relate the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of the energy and temperature scales, plus similar historical setting of the value of the [[mole (unit)|molar scale]] used for the counting of particles. The last factor is not a consideration in the value of the [[Boltzmann constant]], which does a similar job of equating linear energy and temperature scales.
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| The gas constant value is
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| :<math>R=8.314\,4621(75)~\frac{\mathrm{J}}{\mathrm{mol~K}}</math><ref name="CODATA10" /> | |
| The two digits in [[Bracket|parentheses]] are the [[measurement uncertainty|uncertainty]] ([[standard deviation]]) in the last two digits of the value. The relative uncertainty is 9.1{{e|−7}}.
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| Some have suggested that it might be appropriate to name the symbol ''R'' the '''Regnault constant''' in honor of the [[French people|French]] [[chemist]] [[Henri Victor Regnault]], whose accurate experimental data was used to calculate the early value of the constant; however, the exact reason for the original representation of the constant by the letter ''R'' is elusive.<ref name="Jensen">{{cite journal
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| |url= http://pubs.acs.org/doi/abs/10.1021/ed080p731
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| |title=The Universal Gas Constant ''R''
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| |last=Jensen
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| |first=William B.
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| |journal= J. Chem. Educ.
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| |volume= 80
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| |issue= 7
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| |date=July 2003
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| |pages=731
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| |doi=10.1021/ed080p731|bibcode = 2003JChEd..80..731J }}</ref>
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| <ref name="JensenReprint">{{cite web
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| |url= http://www.che.uc.edu/jensen/W.%20B.%20Jensen/Reprints/100.%20Gas%20Constant.pdf
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| |title=Ask the Historian: The Universal Gas Constant - Why is it represented by the letter ''R''?}}</ref>
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| The gas constant occurs in the [[ideal gas law]], as follows:
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| :<math>PV = nRT = m R_{\rm specific} T \,\!</math>
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| where ''P'' is the absolute [[pressure]] (SI unit pascals), ''V'' is the volume of gas (SI unit cubic metres), ''n'' is the [[amount of substance|chemical amount]] of gas (SI unit moles), ''m'' is the [[mass]] (SI unit kilograms) contained in ''V'', and ''T'' is the [[thermodynamic temperature]] (SI unit kelvins). The gas constant is expressed in the same physical units as molar [[entropy]] and molar [[heat capacity]].
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| ==Dimensions of ''R''==
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| From the general equation ''PV'' = ''nRT'' we get
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| :''R'' = ''PV''/''nT'' or (pressure × volume) / (amount × temperature).
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| As pressure is defined as force per unit area, we can also write the gas equation as
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| :''R'' = [(force/area) × volume] / (amount × temperature).
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| Area and volume are simply (length)<sup>2</sup> and (length)<sup>3</sup>. Therefore,
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| :''R'' = [force / (length)<sup>2</sup>] (length)<sup>3</sup> / (amount × temperature).
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| Since force × length = work,
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| :''R'' = (work) / (amount × temperature).
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| The physical significance of ''R'' is work per degree per mole. It may be expressed in any set of units representing work or energy (such as joules), other units representing degrees of temperature (such as degrees Celsius or Fahrenheit), and any system of units designating a mole or a similar pure number that allows an equation of macroscopic mass and fundamental particle numbers in a system, such as an ideal gas (see [[Avogadro's number]]).
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| Instead of a mole the constant can be expressed by considering the [[normal cubic meter]].
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| ==Relationship with the Boltzmann constant==
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| The [[Boltzmann constant]] ''k''<sub>B</sub> (often abbreviated ''k'') may be used in place of the gas constant by working in pure particle count, ''N'', rather than amount of substance, ''n'', since
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| :<math>\qquad R = N_{\rm A} k_{\rm B},\,</math>
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| where ''N''<sub>A</sub> is the [[Avogadro constant]].
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| For example, the ideal gas law in terms of Boltzmann's constant is
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| :<math>PV = N k_{\rm B} T.\,\!</math>
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| where ''N'' is the number of particles (molecules in this case).
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| ==Measurement==
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| As of 2006, the most precise measurement of ''R'' is obtained by measuring the [[speed of sound]] ''c''<sub>a</sub>(''p'', ''T'') in [[argon]] at the temperature ''T'' of the triple point of water (used to define the [[kelvin]]) at different [[pressure]]s ''p'', and [[extrapolation|extrapolating]] to the zero-pressure limit ''c''<sub>a</sub>(0, ''T''). The value of ''R'' is then obtained from the relation
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| :<math>c_\mathrm{a}^2(0, T) = \frac{\gamma_0 R T}{A_\mathrm{r}(\mathrm{Ar}) M_\mathrm{u}},</math>
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| where:
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| *''γ''<sub>0</sub> is the [[heat capacity ratio]] (5/3 for monatomic gases such as argon);
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| *''T'' is the temperature, ''T''<sub>TPW</sub> = 273.16 K by definition of the kelvin;
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| *''A''<sub>r</sub>(Ar) is the relative atomic mass of argon and ''M''<sub>u</sub> = 10<sup>−3</sup> kg mol<sup>−1</sup>.<ref name="CODATA" />
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| ==Specific gas constant==
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| {| class="wikitable" style="float: right;"
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| ! ''R''<sub>specific</sub><br />for dry air
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| ! Units
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| |-
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| | 287.058
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| | J kg<sup>−1</sup> K<sup>−1</sup>
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| |-
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| | 53.3533
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| | ft [[Pound-force|lbf]] [[Pound (mass)|lb]]<sup>−1</sup> °R<sup>−1</sup>
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| |-
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| | 1716.49
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| | ft [[Pound-force|lbf]] [[slug (mass)|slug]]<!--sub m serves no purpose; the (mass) in the article name is for disambiguation from the animals and other things; there is only one unit of measure called a slug--><sup>−1</sup> °R<sup>−1</sup>
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| |-
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| | colspan=2 | <small>Based on a mean molar mass<br />for dry air of 28.9645 g/mol.</small>
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| |-
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| |}
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| The '''specific gas constant''' of a gas or a mixture of gases (''R''<sub>specific</sub>) is given by the molar gas constant, divided by the [[molar mass]] (''M'') of the gas/mixture.
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| :<math> R_{\rm specific} = \frac{R}{M} </math>
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| Just as the ideal gas constant can be related to the Boltzmann constant, so can the specific gas constant by dividing the Boltzmann constant by the molecular mass of the gas.
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| :<math> R_{\rm specific} = \frac{k_{\rm B}}{m} </math>
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| Another important relationship comes from thermodynamics. [[Julius Robert von Mayer|Mayer]]'s relation relates the specific gas constant to the specific heats for a calorically perfect gas and a thermally perfect gas.
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| :<math> R_{\rm specific} = c_{\rm p} - c_{\rm v}\ </math>
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| where ''c<sub>p</sub>'' is the specific heat for a constant pressure and ''c<sub>v</sub>'' is the specific heat for a constant volume.<ref>Anderson, ''Hypersonic and High-Temperature Gas Dynamics'', AIAA Education Series, 2nd Ed, 2006</ref>
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| It is common, especially in engineering applications, to represent the specific gas constant by the symbol ''R''. In such cases, the universal gas constant is usually given a different symbol such as <u style="font-style:italic; text-decoration:overline">R</u> to distinguish it. In any case, the context and/or units of the gas constant should make it clear as to whether the universal or specific gas constant is being referred to.<ref>Moran and Shapiro, ''Fundamentals of Engineering Thermodynamics'', Wiley, 4th Ed, 2000</ref>
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| ==U.S. Standard Atmosphere==
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| The [[U.S. Standard Atmosphere]], 1976 (USSA1976) defines the gas constant ''R''* as:<ref>{{cite web |url=http://www.sworld.com.au/steven/space/atmosphere/ |title=Standard Atmospheres |accessdate=2007-01-07}}</ref><ref name="USSA1976">[http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539_1977009539.pdf U.S. Standard Atmosphere], 1976, U.S. Government Printing Office, Washington, D.C., 1976 (Linked file is 17 MB).</ref>
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| :<math>R^* = 8.314\,32\times 10^3 \frac{\mathrm{N\,m}}{\mathrm{kmol\,K}}. </math>
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| The USSA1976 does recognize, however, that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant.<ref name="USSA1976"/> This disparity is not a significant departure from accuracy, and USSA1976 uses this value of ''R*'' for all the calculations of the standard atmosphere. When using the [[International Organization for Standardization|ISO]] value of ''R'', the calculated pressure increases by only 0.62 [[pascal (unit)|pascal]] at 11 kilometers (the equivalent of a difference of only 17.4 centimeters or 6.8 inches) and an increase of 0.292 Pa at 20 km (the equivalent of a difference of only 0.338 m or 13.2 in).{{Citation needed|date=December 2008}}
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| == Individual gas constants ==
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| Individual gas constants in base SI units of J/kg.K can also be derived for any gas species, by making use of their [[molar mass]].<ref>[http://www.engineeringtoolbox.com/individual-universal-gas-constant-d_588.html Individual Individual Gas Constants and the Universal Gas Constant] — Engineering Toolbox</ref> An average value could also be derived for gas mixtures. Use of individual gas constants may make it more difficult to follow the workings of a calculation, as the relevant values tend to be less well known, and less intuitive, than the fixed value of the universal gas constants, and the well-known values of gas molecular masses.
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| ==References==
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| <!--See [[Wikipedia:Footnotes]] for an explanation of how to generate footnotes using the <ref(erences/)> tags-->
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| <references />
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| == External links ==
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| * ''[http://calculator.tutorvista.com/chemistry/567/ideal-gas-law-calculator.html Ideal gas calculator]'' - Ideal gas calculator provides the correct information for the moles of gas involved.
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| * [http://www.engineeringtoolbox.com/individual-universal-gas-constant-d_588.html Individual Gas Constants and the Universal Gas Constant] — Engineering Toolbox
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| {{DEFAULTSORT:Gas Constant}}
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| [[Category:Ideal gas]]
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| [[Category:Physical constants]]
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| [[Category:Amount of substance]]
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