Gas constant

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The gas constant (also known as the molar, universal, or ideal gas constant, denoted by the symbol R or 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

The two digits in parentheses are the uncertainty (standard deviation) in the last two digits of the value. The relative uncertainty is 1.8×10−6.

The gas constant occurs in the ideal gas law, as follows:

where P is the absolute pressure, V is the volume of gas, n is the number of moles of gas, and T is thermodynamic temperature. The gas constant has the same units as molar entropy.

Contents

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

where NA is the Avogadro constant. For example, the ideal gas law in terms of Boltzmann's constant is

Measurement

As of 2006, the most precise[citation needed] measurement of R is obtained by measuring the speed of sound ca(p, T) in argon at the temperature T of the triple point of water (used to define the kelvin) at different pressures p, and extrapolating to the zero-pressure limit ca(0, T). The value of R is then obtained from the relation

where:

  • γ0 is the heat capacity ratio (5/3 for monatomic gases such as argon);
  • T is the temperature, TTPW = 273.16 K by definition of the kelvin;
  • Ar(Ar) is the relative atomic mass of argon and Mu = 10−3 kg mol−1.[1]

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