Boltzmann constant

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.

5 Must Know Facts For Your Next Test

1. The Boltzmann constant provides a bridge between macroscopic and microscopic physics by linking temperature to energy at the particle level.
2. It appears in the equation for the ideal gas law when expressed as $PV = Nk_B T$, where $N$ is the number of molecules.
3. $k_B$ 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.
4. In units, the Boltzmann constant is measured in joules per kelvin (J/K).
5. 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.