The Boltzmann constant ($k_B$) is a physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. It provides a bridge between macroscopic and microscopic physics.
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The value of the Boltzmann constant is approximately $1.38 \times 10^{-23}$ J/K.
It appears in the equation for the ideal gas law when expressed in terms of individual molecules: $PV = Nk_BT$.
The Boltzmann constant can be used to express entropy at the microscopic level with the formula $S = k_B \ln \Omega$, where $\Omega$ is the number of microstates.
It plays a crucial role in statistical mechanics, particularly in relating temperature to molecular energy distributions.
The unit of the Boltzmann constant is Joules per Kelvin (J/K).
Review Questions
What is the numerical value and unit of the Boltzmann constant?
How does the Boltzmann constant relate to the ideal gas law on a molecular level?
In what equation does the Boltzmann constant appear when expressing entropy?