Boltzmann constant

Definition

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.

5 Must Know Facts For Your Next Test

1. The value of the Boltzmann constant is approximately $1.38 \times 10^{-23}$ J/K.
2. It appears in the equation for the ideal gas law when expressed in terms of individual molecules: $PV = Nk_BT$.
3. 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.
4. It plays a crucial role in statistical mechanics, particularly in relating temperature to molecular energy distributions.
5. 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?

Related terms

Ideal Gas Law: An equation of state for an ideal gas which relates pressure, volume, and temperature: $PV = nRT$.

Entropy: A measure of disorder or randomness in a system, often expressed with units involving kB.

Statistical Mechanics: A branch of physics that uses statistics to describe and predict properties of systems composed of large numbers of particles.