Definition

1. Noun:
   • A fundamental physical constant: Boltzmann's constant is a physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. It is a key parameter in statistical mechanics and thermodynamics.

Usage Examples

• Noun:
  • The value of Boltzmann's constant is approximately 1.380649 × 10⁻²³ joules per kelvin.
  • In the formula for entropy, Boltzmann's constant appears as a scaling factor.

Advanced Usage

• In the Boltzmann entropy formula: Boltzmann's constant is central to the definition of entropy in statistical mechanics, expressed as S = kB ln Ω, where kB is Boltzmann's constant and Ω is the number of microstates.

  • The profound equation S = k_B ln Ω is engraved on Ludwig Boltzmann's tombstone.

• In the ideal gas law: Boltzmann's constant provides the microscopic connection in the kinetic theory of gases, linking pressure and volume to temperature.

  • The product of the Boltzmann constant and Avogadro's number yields the ideal gas constant.

Variants and Related Words

• Boltzmann factor (n): A weighting factor that determines the relative probability of a system being in a certain state, given by exp(-E/(kB T)), where kB is Boltzmann's constant.

  • The Boltzmann factor is crucial for calculating population distributions in thermal equilibrium.

• Stefan-Boltzmann constant (n): A derived constant in the law for thermal radiation, related to but distinct from Boltzmann's constant.

  • The Stefan-Boltzmann constant is denoted by σ and is derived using Boltzmann's constant.

Synonyms

• k_B: The standard symbol for Boltzmann's constant.
• Boltzmann constant: An alternative naming with the same meaning.

Related Phrases

• Boltzmann's constant times temperature: Often appears as the thermal energy scale, k
  • At room temperature, kB T is about 4.11 × 10⁻²¹ joules.

Related Concepts

• Ideal gas constant: The molar gas constant R, which is equal to Boltzmann's constant multiplied by Avogadro's number (R = kA).
• Thermodynamic beta: Defined as β = 1/(k_B T), a parameter frequently used in statistical mechanics.

Noun

1. constant used in the calculation of the ideal gas constant