Boltzmann distribution law

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Thân thiện
Definition
  1. Noun:
    • A statistical law in physics: The Boltzmann distribution law is a fundamental principle that describes the statistical distribution of energy among a large number of identical particles (such as molecules in a gas) that are in a state of thermal equilibrium at a given absolute temperature.
Usage
  • The Boltzmann distribution law is used to calculate the probability that a particle will be in a particular energy state. It is central to statistical mechanics and thermodynamics.
  • It is typically applied to systems in thermal contact with a heat reservoir, where the temperature is constant.
Examples
  • Noun:
    • According to the Boltzmann distribution law, the number of molecules with a specific energy decreases exponentially as that energy increases.
    • Understanding the Boltzmann distribution law is essential for explaining phenomena like specific heat capacities and reaction rates.
Advanced Usage
  • "To obey the Boltzmann distribution law": Describes a system whose particles follow this statistical energy distribution.
    • At thermal equilibrium, the particles in the gas can be said to obey the Boltzmann distribution law.
  • "Derived from the Boltzmann distribution law": Indicates a formula or conclusion that is a direct mathematical result of this law.
    • The Maxwell-Boltzmann speed distribution is derived from the Boltzmann distribution law.
Variants and Related Words
  • Boltzmann factor (n): The exponential term (e^(-E/kT)) in the distribution law that gives the relative probability of a state with energy E.
    • The Boltzmann factor shows how temperature influences the population of energy levels.
  • Maxwell-Boltzmann distribution (n): A specific application of the law describing the distribution of particle speeds in an ideal gas.
    • The Maxwell-Boltzmann distribution predicts the most probable speed of gas molecules.
Synonyms
  • Boltzmann statistics: Often used interchangeably in the context of classical, distinguishable particles.
  • Canonical distribution: A more general term in statistical mechanics for a system in thermal equilibrium with a heat bath, which for classical particles yields the Boltzmann distribution.
Related Phrases
  • "Governed by the Boltzmann distribution": A phrase describing a system whose state populations are determined by this law.
    • The relative populations of the excited states in the sample are governed by the Boltzmann distribution.
Noun
  1. (physics) a law expressing the distribution of energy among the molecules of a gas in thermal equilibrium

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