Boltzmann constant

The Boltzmann constant converts temperature into energy per particle and sets the scale linking microscopic particle behavior to macroscopic thermodynamics. Its SI value is exactly 1.380649 × 10⁻²³ joules per kelvin.

Ideal gas law: An equation relating pressure, volume, amount, and temperature for an idealized gas. In its particle form, the law uses the Boltzmann constant to relate pressure and temperature.
Boltzmann distribution: A probability distribution giving the equilibrium occupation of states with different energies at a specified temperature. The factor kT determines how strongly higher-energy states are suppressed.
Ludwig Boltzmann: An Austrian physicist whose work established statistical mechanics and a statistical interpretation of entropy. The constant honors the physicist whose ideas connected microscopic states with thermodynamic entropy.
Gas constant: The molar energy-per-temperature constant equal to the Boltzmann constant multiplied by Avogadro’s constant. It performs the analogous temperature-to-energy conversion for a mole rather than one particle.
Equipartition theorem: A statistical-mechanical result assigning average energy of one-half kT to each quadratic degree of freedom at thermal equilibrium. The constant k sets the average thermal energy assigned to each degree of freedom.
Boltzmann entropy formula: The statistical relation S = k ln W between entropy and the number of compatible microstates. It makes k the conversion factor between information about microstates and thermodynamic entropy.
Max Planck: A German theoretical physicist who introduced energy quantization and helped establish quantum theory. Planck introduced the constant’s modern notation and helped define its role in statistical physics.
Avogadro constant: The exact number of specified elementary entities in one mole, 6.02214076 × 10²³. Multiplying it by k gives the gas constant, converting particle-scale quantities to molar ones.
Arrhenius equation: An equation describing how a reaction rate depends on temperature and activation energy. Its exponential temperature dependence uses the ratio of activation energy to kT.
Partition function: A sum over a system’s possible states that encodes its equilibrium thermodynamic properties. Temperature enters its state weights through energy divided by kT.

Linked from 35 pages