Molar gas constant: Difference between revisions
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In [[chemistry]], [[chemical engineering]] and [[physics]], the '''molar gas constant''' (also called '''universal gas constant''') '''R''' is a fundamental physical constant which appears in a large number of fundamental equations in the physical sciences, such as the [[ideal gas law]] and other [[Equation of state|equations of state]] and the [[Nernst equation]]. It is equivalent to | In [[chemistry]], [[chemical engineering]] and [[physics]], the '''molar gas constant''' (also called '''universal gas constant''') '''R''' is a fundamental physical constant which appears in a large number of fundamental equations in the physical sciences, such as the [[ideal gas law]] and other [[Equation of state|equations of state]] and the [[Nernst equation]]. It is equivalent to the [[Boltzmann constant]] (''k<sub>B</sub>'') times [[Avogadro's constant]] (''N''): ''R'' = ''k''<sub>B</sub>''N''<sub>A</sub>. | ||
Currently its most accurate value is:<ref>[http://physics.nist.gov/cgi-bin/cuu/Value?r Molar gas constant] Obtained on January 19, 2012 from the [[NIST]] website</ref> | Currently its most accurate value is:<ref>[http://physics.nist.gov/cgi-bin/cuu/Value?r Molar gas constant] Obtained on January 19, 2012 from the [[NIST]] website</ref> | ||
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==The specific gas constant== | ==The specific gas constant== | ||
The gas constant of a specific gas, as differentiated from the above universal molar gas constant which applies for any ideal gas, is designated by the symbol '''''R'''''<sub>s</sub> and is equal to the molar gas constant divided by the molecular mass ('''''M''''') of the gas: | The gas constant of a specific gas, as differentiated from the above universal molar gas constant which applies for any ideal gas, is designated by the symbol '''''R'''''<sub>s</sub> and is equal to the molar gas constant divided by the molecular mass ('''''M''''') of the gas: | ||
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==The U.S. Standard Atmosphere's gas constant== | ==The U.S. Standard Atmosphere's gas constant== | ||
The U.S. Standard Atmosphere is an idealized representation of the Earth's atmosphere from the surface to an altitude of 1,000 kilometers during a period in which solar activity is assumed to be moderate.<ref name=NASA>[http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539_1977009539.pdf U.S. Standard Atmosphere 1976], Table 2, PDF page 18 of 241 PDF pages, from the website of the National Aeronautics and Space Administration (NASA).</ref><ref>[http://www.sworld.com.au/steven/space/atmosphere/ Standard Atmospheres], lists a few errors found in the U.S. Standard Atmosphere 1976, including the value of R.</ref> | The U.S. Standard Atmosphere is an idealized representation of the Earth's atmosphere from the surface to an altitude of 1,000 kilometers during a period in which solar activity is assumed to be moderate.<ref name=NASA>[http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539_1977009539.pdf U.S. Standard Atmosphere 1976], Table 2, PDF page 18 of 241 PDF pages, from the website of the National Aeronautics and Space Administration (NASA).</ref><ref>[http://www.sworld.com.au/steven/space/atmosphere/ Standard Atmospheres], lists a few errors found in the U.S. Standard Atmosphere 1976, including the value of R.</ref> | ||
Revision as of 15:14, 14 October 2013
| Values of R | Units |
|---|---|
| 8.3144621 | J·K-1·mol-1 |
| 0.082057 | L·atm·K-1·mol-1 |
| 8.205736 × 10-5 | m3·atm·K-1·mol-1 |
| 8.3144621 | L·kPa·K-1·mol-1 |
| 8.3144621 | m3·Pa·K-1·mol-1 |
| 62.36368 | L·mmHg·K-1·mol-1 |
| 62.36359 | L·torr·K-1·mol-1 |
| 83.144621 | L·mbar·K-1·mol-1 |
| 10.73158 | ft3·psi· °R-1·lb-mol-1 |
| 0.73024 | ft3·atm·°R-1·lb-mol-1 |
In chemistry, chemical engineering and physics, the molar gas constant (also called universal gas constant) R is a fundamental physical constant which appears in a large number of fundamental equations in the physical sciences, such as the ideal gas law and other equations of state and the Nernst equation. It is equivalent to the Boltzmann constant (kB) times Avogadro's constant (N): R = kBNA.
Currently its most accurate value is:[1]
- R = 8.3144621 J · K-1 · mol-1
The gas constant occurs in the ideal gas law as follows:
where:
- P is the gas absolute pressure
- T is the gas absolute temperature
- V is the volume the gas occupies
- n is the number of moles of gas
- Vm is the molar volume
The specific gas constant
The gas constant of a specific gas, as differentiated from the above universal molar gas constant which applies for any ideal gas, is designated by the symbol Rs and is equal to the molar gas constant divided by the molecular mass (M) of the gas:
- Rs = R ÷ M
The specific gas constant for an ideal gas may also be obtained from the following thermodynamics relationship:[2]
- Rs = cp – cv
where cp and cv are the gas's specific heats at constant pressure and constant volume respectively.
Some example values of the specific gas constant are:
- Ammonia (molecular mass of 17.032 g · mol–1) : Rs = 0.4882 J · K–1 · g–1
- Hydrogen (molecular mass of 2.016 g · mol–1) : Rs = 4.1242 J · K–1 · g–1
- Methane (molecular mass of 16.043 g · mol–1) : Rs = 0.5183 J · K–1 · g–1
Unfortunately, many authors in the technical literature sometimes use R as the specific gas constant without designating it as such or stating that it is the specific gas constant. This can and does lead to confusion for many readers.
The U.S. Standard Atmosphere's gas constant
The U.S. Standard Atmosphere is an idealized representation of the Earth's atmosphere from the surface to an altitude of 1,000 kilometers during a period in which solar activity is assumed to be moderate.[3][4]
It consists of a number of models that define values for atmospheric temperature, pressure, density and other properties over that range of altitudes. The first model was published in 1958 by the United States Committee on Extension to the Standard Atmosphere (COESA), and was updated in 1962, 1966, and 1976.
The U.S. COESA models make use of the molar gas constant which is designated as R* and defined as having a value of:
- R* = 8.31432 x 103 N · m · kmol–1 · K–1
which is equivalent to:
- R* = 8.31432 J · K–1 · mol–1
The U.S. COESA realizes that their value of R* differs from NIST's 2010 value of R = 8.3144621 J · K · mol–1 but the difference is evidently deemed not to be significant for their purposes.[3]
Reference
- ↑ Molar gas constant Obtained on January 19, 2012 from the NIST website
- ↑ Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner and Margaret B. Bailey (2010), Fundamentals of Engineering Thermodynamics, 7th Edition, Wiley, page 131, ISBN: 0-470-49590-1.
- ↑ 3.0 3.1 U.S. Standard Atmosphere 1976, Table 2, PDF page 18 of 241 PDF pages, from the website of the National Aeronautics and Space Administration (NASA).
- ↑ Standard Atmospheres, lists a few errors found in the U.S. Standard Atmosphere 1976, including the value of R.