The gas constant is denoted by the symbol or. It is equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole, i.e. the pressure–volume product, 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. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation. Physically, the gas constant is the constant of proportionality that relates 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 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. The gas constant R is defined as the Avogadro constantNA multiplied by the Boltzmann constant k: Since the 2019 redefinition of SI base units, which came into effect on 20 May 2019, both NA and k are defined with exact numerical values when expressed in SI units. As a consequence, the value of the gas constant is also exactly defined, at precisely. Some have suggested that it might be appropriate to name the symbol R the Regnault constant in honour of the FrenchchemistHenri Victor Regnault, whose accurate experimental data were used to calculate the early value of the constant; however, the origin of the letter R to represent the constant is elusive. 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 amount of gas, m is the mass contained in V, and T is the thermodynamic temperature. Rspecific is the mass-specific gas constant. The gas constant is expressed in the same physical units as molar entropy and molar heat capacity.
Dimensions
From the ideal gas lawPV = nRT we get: where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature. As pressure is defined as force per unit area, the gas equation can also be written as: Area and volume are 2 and 3 respectively. Therefore: Since force × length = work: The physical significance of R is work per degree per mole. It may be expressed in any set of units representing work or energy, units representing degrees of temperature on an absolute scale, 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. Instead of a mole the constant can be expressed by considering the normal cubic meter. Otherwise, we can also say that: Therefore, we can write R as: And so, in SI base units:
Relationship with the Boltzmann constant
The Boltzmann constant kB may be used in place of the gas constant by working in pure particle count, N, rather than amount of substance, n, since where NA is the Avogadro constant. For example, the ideal gas law in terms of Boltzmann's constant is where N is the number of particles, or to generalize to an inhomogeneous system the local form holds: where n is the number density.
Measurement and replacement with defined value
As of 2006, the most precise measurement of R had been obtained by measuring the speed of soundca in argon at the temperature T of the triple point of water at different pressures P, and extrapolating to the zero-pressure limit ca. The value of R is then obtained from the relation where:
The specific gas constant of a gas or a mixture of gases is given by the molar gas constant divided by the molar mass of the gas or mixture. 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. Another important relationship comes from thermodynamics. Mayer's relation relates the specific gas constant to the specific heats for a calorically perfect gas and a thermally perfect gas. where cp is the specific heat for a constant pressure and cv is the specific heat for a constant volume. 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 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.
The U.S. Standard Atmosphere, 1976 defines the gas constant R∗ as: Note the use of kilomole units resulting in the factor of 1,000 in the constant. The USSA1976 acknowledges that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant. 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 pascal at 11 kilometers and an increase of 0.292 Pa at 20 km. Also note that this was well before the 2019 SI redefinition which gave the constant an exact value.
