Gas constant

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Values of R Units
8.314472 J · K-1 · mol-1
0.0820574587 L · atm · K-1 · mol-1
8.20574587 x 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
6.132439833 lbf · ft · K-1 · g · mol-1
10.7316 ft³ · psi · °R-1 · lb-mol-1
8.63 x 10-5 eV · K-1 · atom-1
0.7302 ft3·atm·°R-1·lb-mole-1

The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. It is another name for the Boltzmann constant, but when used in the ideal gas law it is usually expressed in the more convenient units of energy per kelvin per mole rather than simply energy per kelvin per particle.

The gas constant occurs in the simplest equation of state, the ideal gas law, as follows:

P = {RT\over{\tilde{V}}}

where P is the pressure of an ideal gas
T is its temperature
\tilde{V} is its molar volume
This can also be written as:

\qquad PV=nRT

where V is the volume the gas occupies
n is the moles of gas

R appears in the Nernst equation as well as in the Lorentz-Lorenz formula.

Its value is:

R = 8.314472(15) J · K-1 · mol-1

The two digits between the parentheses denote the uncertainty (standard deviation) in the last two digits of the value.

Contents

[edit] Boltzmann constant

The Boltzmann constant kB (often abbreviated k) may be used in place of the other forms of the ideal gas constant by working in pure particle count rather than number of moles of gas; this simply requires carrying a factor of Avogadro's number. Writing:

k_B = \frac{R}{N_A}

One can then express the ideal gas law in direct terms of Boltzmann's constant:

\qquad PV=Nk_BT

with N = nNA is the actual number of molecules.

[edit] Specific gas constant

The specific gas constant of a gas or a mixture of gases ( \bar{R} ) is given by the universal gas constant, divided by the molar mass ( M ) of the gas/mixture.

\bar{R} = \frac{R}{M}

It is common to represent the specific gas constant by the symbol R. In such cases the context and/or units of R 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.

[edit] US Standard Atmosphere

The US Standard Atmosphere, 1976 (USSA1976) defines the Universal Gas Constant (R) as:[1][2]

R = 8.31432\mbox{ x }10^3 \frac{\mathrm{N \cdot m}}{\mathrm{kmol \cdot K}}

The USSA1976 does recognize, however, that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant.[2] Still, the USSA1976 uses this value of R for all the calculations of the standard atmosphere. This disparity is not a significant departure from accuracy. 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).

[edit] See also

[edit] References

  1. ^ Standard Atmospheres. Retrieved on January 7, 2007.
  2. ^ a b U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976 (Linked file is 17 MiB).

[edit] External links

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