# Boltzmann’s Constant

**Episode #8 of the c****ourse “Most important numbers in the world”**

**1.3806488(13)×10 ^{−23 }joule per kelvin**

The Boltzmann Constant is one of the fundamental numbers describing an essentially important relationship in molecular thermodynamics and statistical mechanics. The number was discovered and described by Austrian physicist Ludwig Boltzmann, and it is a ratio that identifies how energy in a particle is related to the temperature of the particle and of the entire substance. The constant number describes how gas temperature changes per particle affect the temperature change in the entire substance, often measured in increments of “moles.” Therefore, Boltzmann’s Constant is equal to the Gas Constant (R) divided by Avogadro’s Constant (*N*_{A}), and is expressed as:

*K*_{B} = R / *N*_{A}

Because the Boltzmann Constant is expressed in terms of energy divided by temperature, it is likened to the expression of entropy. Boltzmann’s Constant has been key to understanding how the microstates of a system are interrelated to its macrostates and the proportions at which change happens. This essential number links the statistical mechanics of entropy to the classical understanding of thermodynamic entropy.

In a thermodynamic system, atoms and molecules behave independently with various properties that allow energy and heat distribution. The thermodynamics of molecular physics contributes to the larger physical properties of the substances, and Boltzmann’s Constant is a model of classical statistical mechanics that holds true and predicts properties for molecular speeds in a gas.

Although Boltzmann’s work had begun to link the ideas of probability and entropy in the late 19th century, it was nearly 30 years later that Max Planck’s work and 20th century experiments based on Albert Einstein’s theories confirmed their relation. It was actually Planck who thought to give an exact number to the constant value, and in his Nobel Prize acceptance speech pointed that out.

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