[5], 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 R to distinguish it. Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure p and volume V is proportional to the product of amount of substance n (in moles) and absolute temperature T: where R is the gas constant (8.31446261815324 J⋅K−1⋅mol−1). endstream endobj startxref Based on these measurements, the CODATA recommended 1.380 649 × 10−23 J⋅K−1 to be the final fixed value of the Boltzmann constant to be used for the International System of Units.[15]. As pressure is defined as force per unit area, the gas equation can also be written as: Area and volume are (length)2 and (length)3 respectively. However, following the 2019 redefinition of the SI base units, R now has an exact value defined in terms of other precisely defined physical constants. The gas constant (also known as the molar gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole, i.e. Therefore: The physical significance of R is work per degree per mole. Such is its importance that it is inscribed on Boltzmann's tombstone. Another important relationship comes from thermodynamics. Note the use of kilomole units resulting in the factor of 1,000 in the constant. The gas constant is expressed in the same physical units as molar entropy and molar heat capacity. In physics research another definition is often encountered in setting k to unity, resulting in the Planck units or natural units for temperature and energy. endstream endobj 14 0 obj <>stream [2] As a consequence, the value of the gas constant is also exactly defined, at precisely 8.31446261815324 J⋅K−1⋅mol−1. When using the ISO value of R, the calculated pressure increases by only 0.62 pascal at 11 kilometers (the equivalent of a difference of only 17.4 centimeters or 6.8 inches) and an increase of 0.292 Pa at 20 km (the equivalent of a difference of only 33.8 cm or 13.2 in).

The constant of proportionality k serves to make the statistical mechanical entropy equal to the classical thermodynamic entropy of Clausius: One could choose instead a rescaled dimensionless entropy in microscopic terms such that. 0 [13][14] This decade-long effort was undertaken with different techniques by several laboratories;[a] it is one of the cornerstones of the 2019 redefinition of SI base units. Sign-Up Today! Involved laboratories cited by CODATA in 2017: The value is exact but not expressible as a finite decimal; approximated to 9 decimal places only. Considering that the translational motion velocity vector v has three degrees of freedom (one for each dimension) gives the average energy per degree of freedom equal to one third of that, i.e.

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