College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
The Boltzmann constant ($k_B$) is a fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. It is central to the kinetic theory of gases and has a value of approximately $1.38 \times 10^{-23}$ J/K.
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The Boltzmann constant provides a bridge between macroscopic and microscopic physics by linking temperature to energy at the particle level.
It appears in the equation for the ideal gas law when expressed as $PV = Nk_B T$, where $N$ is the number of molecules.
$k_B$ is used in defining entropy through Boltzmann's entropy formula: $S = k_B \ln \Omega$, where $\Omega$ is the number of microstates corresponding to a macrostate.
In units, the Boltzmann constant is measured in joules per kelvin (J/K).
The value of Boltzmann constant also appears in Planck's law, which describes the spectral density of electromagnetic radiation emitted by a black body.
Review Questions
What role does the Boltzmann constant play in relating temperature to kinetic energy?
How does the Boltzmann constant appear in the ideal gas law?
What are the units of measurement for the Boltzmann constant?
Related terms
Ideal Gas Law: An equation of state for an ideal gas, given as $PV = Nk_B T$, relating pressure (P), volume (V), number of molecules (N), and temperature (T).
Kinetic Theory of Gases: A theory that models gases as collections of many small particles whose motions obey Newton's laws and provides insight into concepts like temperature and pressure.
Entropy: A measure of disorder or randomness in a system, often represented by $S = k_B \ln \Omega$, where $\Omega$ represents possible microstates.