# Boltzmann constant

Boltzmann’s constant throws a bridge from the macrocosm to the microcosm, linking temperature with the kinetic energy of molecules.

Ludwig Boltzmann is one of the founders of the molecular kinetic theory of gases, on which the modern picture of the relationship between the motion of atoms and molecules, on the one hand, and the macroscopic properties of matter, such as temperature and pressure, on the other, is based. Within the framework of this picture, the gas pressure is due to the elastic collisions of gas molecules against the walls of the vessel, and the temperature is due to the speed of the molecules (or rather, their kinetic energy). The faster the molecules move, the higher the temperature.

Boltzmann’s constant makes it possible to directly relate the characteristics of the microcosm with the characteristics of the macrocosm – in particular, with the readings of a thermometer. Here is the key formula that establishes this ratio:

1/2 mv2 = kT

Where m and v – respectively, the mass and average velocity of the gas molecules, T – gas temperature (in absolute Kelvin scale), and k – Boltzmann’s constant. This equation creates a bridge between the two worlds, linking the characteristics of the atomic level (on the left) with bulk properties (on the right) that can be measured with human instruments, in this case thermometers. This connection is provided by the Boltzmann constant kequal to 1.38 x 10–23 J / C

The branch of physics that studies the connections between the phenomena of the microcosm and the macrocosm is called statistical mechanics. There is hardly an equation or formula in this section that does not include the Boltzmann constant. One of these relations was deduced by the Austrian himself, and it is simply called Boltzmann equation:

S = k log p + b

Where S – entropy of the system (cm. The second law of thermodynamics), p – so-called statistical weight (a very important element of the statistical approach), and b Is another constant.

Throughout his life, Ludwig Boltzmann was literally ahead of his time, developing the foundations of the modern atomic theory of the structure of matter, entering into fierce disputes with the overwhelming conservative majority of the modern scientific community, which considered atoms to be only a convention, convenient for calculations, but not objects of the real world. When his statistical approach did not meet with the slightest understanding even after the appearance of special relativity, Boltzmann committed suicide in a moment of deep depression. Boltzmann’s equation is carved on his tombstone.

Ludwig Edward BOLTZMAN
Boltzmann, 1844-1906

Austrian physicist. Born in Vienna into the family of a civil servant. Studied at the University of Vienna on the same course with Joseph Stefan (cm. Stefan-Boltzmann law). Defended in 1866, he continued his scientific career, occupying at various times professorships in the departments of physics and mathematics at the universities of Graz, Vienna, Munich and Leipzig. As one of the main proponents of the reality of the existence of atoms, he made a number of outstanding theoretical discoveries that shed light on how phenomena at the atomic level affect the physical properties and behavior of matter.