Boltzmann constant

The Boltzmann constant (kB or k) is a physical constant named after its discoverer, Ludwig Boltzmann, which relates the average relative kinetic energy of particles in a gas with the temperature of the gas and occurs in Planck's law of black-body radiation and in Boltzmann's entropy formula. It is the gas constant R divided by the Avogadro constant NA: The Boltzmann constant has the dimension energy divided by temperature, the same as entropy. Before 2019, its value in SI units was a measured quantity. Measurements of the Boltzmann constant depended on the definition of the kelvin in terms of the triple point of water. However, in the redefinition of SI base units adopted at the 26th General Conference on Weights and Measures (CGPM) on 16 November 2018, the definition of the kelvin was changed to one based on a fixed, exact numerical value of the Boltzmann constant, similar to the way that the speed of light was given an exact numerical value at the 17th CGPM in 1983. The final value (based on the 2017 CODATA adjusted value of 1.38064903(51)×10−23 J/K) is 1.380649×10−23 J/K. The Boltzmann constant, k, is a scaling factor between macroscopic (thermodynamic temperature) and microscopic (thermal energy) physics. 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 (8.3144598(48) J⋅K−1⋅mol−1). Introducing the Boltzmann constant transforms the ideal gas law into an alternative form: where N is the number of molecules of gas. For n = 1 mol, N is equal to the number of particles in one mole (Avogadro's number). Given a thermodynamic system at an absolute temperature T, the average thermal energy carried by each microscopic degree of freedom in the system is 1/2kT (i.e., about 2.07×10−21 J, or 0.013 eV, at room temperature). In classical statistical mechanics, this average is predicted to hold exactly for homogeneous ideal gases. Monatomic ideal gases (the six noble gases) possess three degrees of freedom per atom, corresponding to the three spatial directions, which means a thermal energy of 3/2kT per atom. This corresponds very well with experimental data. The thermal energy can be used to calculate the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass. The root mean square speeds found at room temperature accurately reflect this, ranging from 1370 m/s for helium, down to 240 m/s for xenon.