Fundamental Physical Constant
1.380649 × 10−23 J/K

The Boltzmann Constant

Bridging the microscopic and macroscopic worlds of physics

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01

What is the Boltzmann Constant?

1.380649
× 10⁻²³ J/K
Exact defined value since 2019
kB
Symbol
Named after Ludwig Boltzmann
7
SI Defining Constants
One of the seven constants that define the SI
02

The Entropy Formula

S = k ln W
S

Entropy

A macroscopic thermodynamic quantity measuring the disorder or randomness of a system.

k

Boltzmann Constant

The proportionality factor linking microscopic probability to macroscopic entropy.

W

Microstates

The number of microscopic configurations corresponding to a given macroscopic state.

03

Bridge Between Two Worlds

🌡

Macroscopic

  • Temperature, pressure, volume
  • Heat and thermodynamics
  • Gas constant R = 8.314 J/(mol·K)
k
The link

Microscopic

  • Atoms and molecules
  • Kinetic energy of particles
  • Avogadro's number NA

Equipartition Theorem

Ideal Gas Law

Fundamental Relationship
R = NA · k

The gas constant R equals Avogadro's number times the Boltzmann constant — connecting molar and molecular scales.

04

Ludwig Boltzmann

1844

Birth in Vienna

Ludwig Eduard Boltzmann is born in Vienna, Austria, into a family of civil servants.

1866

Doctorate

Receives his doctorate from the University of Vienna under Josef Stefan, studying the kinetic theory of gases.

1872

H-Theorem & Boltzmann Equation

Publishes the H-theorem and the Boltzmann transport equation, providing a statistical foundation for the second law of thermodynamics.

1877

Statistical Entropy

Introduces the statistical definition of entropy: S = k ln W, connecting thermodynamic entropy to molecular probability.

1884

Stefan-Boltzmann Law

Derives the Stefan-Boltzmann law for blackbody radiation from thermodynamic principles, confirming his mentor's empirical law.

1894

Prussian Academy

Elected to the Prussian Academy of Sciences, cementing his reputation across Europe.

1906

Passing in Trieste

Dies in Trieste, Italy, at age 62. His gravestone in Vienna bears his greatest equation: S = k log W.

05

The 2019 SI Redefinition

20 May 2019
Before 2019

Triple Point of Water

The kelvin was defined by the triple point of water (273.16 K), dependent on a physical artifact and the isotopic composition of water.

Since 2019

Fixed Constant

The kelvin is defined by fixing the exact value of the Boltzmann constant k = 1.380649 × 10⁻²³ J/K, tying temperature to a fundamental invariant of nature.

Precision Measurement Methods

Acoustic Gas Thermometry Dielectric Constant Gas Thermometry Johnson Noise Thermometry Doppler Broadening Thermometry
06

Applications

💻

Semiconductor Physics

VT = kT/q ≈ 25.9 mV

Blackbody Radiation

B(ν,T) = 2hν³/c² · 1/(e^{hν/kT}−1)
🌌

Cosmology

n(ε) ∝ e^{−ε/kT}

Chemical Kinetics

krate = A · e^{−Eₐ/kT}
📡

Electronic Noise

Vn = √(4kTRΔf)
📊

Information Theory

S = −k Σ pᵢ ln pᵢ
07

Legacy

"

— Ludwig Boltzmann
S = k log W