Gas constant: Difference between revisions
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==Overview== | ==Overview== | ||
The '''gas constant''' (also known as the '''molar''', '''universal''', or '''ideal gas constant''', usually denoted by symbol '''''R''''') is a [[physical constant]] which is featured in a large number of fundamental equations in the physical sciences, such as the [[ideal gas law]] and the [[Nernst equation]]. It is equivalent to the [[Boltzmann constant]], but expressed in units of [[energy]] (i.e. the pressure-volume product) per [[kelvin]] per ''[[mole (unit)|mole]]'' (rather than energy per kelvin per ''particle''). | The '''gas constant''' (also known as the '''molar''', '''universal''', or '''ideal gas constant''', usually denoted by symbol '''''R''''') is a [[physical constant]] which is featured in a large number of fundamental equations in the physical sciences, such as the [[ideal gas law]] and the [[Nernst equation]]. It is equivalent to the [[Boltzmann constant]], but expressed in units of [[energy]] (i.e. the pressure-volume product) per [[kelvin]] per ''[[mole (unit)|mole]]'' (rather than energy per kelvin per ''particle''). | ||
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Latest revision as of 15:26, 9 August 2012
| Values of R | Units (V·P·T-1·n-1) |
|---|---|
| 8.314472 | J·K-1·mol-1 |
| 0.0820574587 | L·atm·K-1·mol-1 |
| 8.20574587 × 10-5 | m3·atm·K-1·mol-1 |
| 8.314472 | cm3·MPa·K-1·mol-1 |
| 8.314472 | L·kPa·K-1·mol-1 |
| 8.314472 | m3·Pa·K-1·mol-1 |
| 62.3637 | L·mmHg·K-1·mol-1 |
| 62.3637 | L·Torr·K-1·mol-1 |
| 83.14472 | L·mbar·K-1·mol-1 |
| 1.987 | cal·K-1·mol-1 |
| 6.132440 | lbf·ft·K-1·g·mol-1 |
| 10.7316 | ft3·psi· °R-1·lb-mol-1 |
| 0.7302 | ft3·atm·°R-1·lb-mol-1 |
| 1716 (Air only) | ft·lb·°R-1·slug-1 |
| 286.9 (Air only) | N·m·kg-1·K-1 |
| 286.9 (Air only) | J·kg-1·K-1 |
| 999 | ft3·mmHg·K-1·lb-mol-1 |
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Overview
The gas constant (also known as the molar, universal, or ideal gas constant, usually denoted by symbol R) is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy (i.e. the pressure-volume product) per kelvin per mole (rather than energy per kelvin per particle).
Its value is:
- R = 8.314472(15) J · K-1 · mol-1
The two digits in parentheses are the uncertainty (standard deviation) in the last two digits of the value.
The gas constant occurs in the simplest equation of state, the ideal gas law, as follows:
- <math>P = \frac{nRT}{V} = \frac{RT}{V_{\rm m}}</math>
where:
- <math>P\,\!</math> is the absolute pressure
- <math>T\,\!</math> is absolute temperature
- <math>V\,\!</math> is the volume the gas occupies
- <math>n\,\!</math> is the amount of gas (the number of gas molecules, usually in moles)
- <math>V_{\rm m}\,\!</math> is the molar volume
The gas constant has the same units as specific entropy.
Relationship with the Boltzmann constant
The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working in pure particle count, N, rather than number of moles, n, since
- <math>\qquad R=N_A k_B\,\!</math>,
where <math>N_A</math> is Avogadro's number. For example, the ideal gas law in terms of Boltzmann's constant is <math>PV=Nk_BT\,\!</math>.
Specific gas constant
The specific gas constant of a gas or a mixture of gases (<math>\bar{R}</math>) is given by the universal gas constant, divided by the molar mass (<math>M</math>) of the gas/mixture.
- <math> \bar{R} = \frac{R}{M} </math>
It is common to represent the specific gas constant by the symbol <math>R</math>. In such cases the context and/or units of <math>R</math> should make it clear as to which gas constant is being referred to. For example, the equation for the speed of sound is usually written in terms of the specific gas constant.
The specific gas constant of dry air is
- <math>\bar R_\mathrm{dry\,air} = 287.05 \frac{\mbox{J}}{\mbox{kg} \cdot \mbox{K}}</math>
US Standard Atmosphere
The US Standard Atmosphere, 1976 (USSA1976) defines the Universal Gas Constant as:[1][2]
- <math>R = 8.31432\times 10^3 \frac{\mathrm{N \cdot m}}{\mathrm{kmol \cdot K}} </math>
The USSA1976 does recognize, however, that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant.[2] 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 ISO value of R, the calculated pressure increases by only 0.62 pascals at 11,000 meters (the equivalent of a difference of only 0.174 meters – or 6.8 inches) and an increase of 0.292 pascals at 20,000 meters (the equivalent of a difference of only 0.338 meters – or 13.2 inches).
See also
References
- ↑ "Standard Atmospheres". Retrieved 2007-01-07.
- ↑ 2.0 2.1 U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976 (Linked file is 17 MiB).
External links
- Gas Constant CODATA Value at NIST
- Boltzmann Constant CODATA Value at NIST