BoltzmannConstant - crowlogic/arb4j GitHub Wiki

Boltzmann's Constant

Boltzmann's constant is a physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. It is denoted by $k$ or $k_B$ and has a value of approximately

$$k_B = 1.380649 \times 10^{-23} \text{m}^2 \text{kg} \text{s}^{-2} \text{K}^{-1}$$

It is named after the Austrian physicist Ludwig Boltzmann and is a fundamental constant used in statistical mechanics and thermodynamics.

• $\text{m}^2$ (square meters): This relates to spatial dimensions or area.
• $\text{kg}$ (kilograms): This is a unit of mass.
• $\text{s}^{-2}$ (per square second): This relates to how things change over time, often acceleration.
• $\text{K}^{-1}$ (per Kelvin): This is a unit of temperature, Kelvin being the unit.

Put together, $\text{m}^2 \text{kg} \text{s}^{-2} \text{K}^{-1}$ essentially links space, mass, time, and temperature together. This makes sense when you consider that Boltzmann's constant is a bridge between the microscopic world (atoms and molecules, characterized by their mass and speed) and the macroscopic world (observable physical systems, like a container of gas, characterized by temperature).

In simple terms, Boltzmann's constant allows you to connect the "jiggling" of individual molecules (their kinetic energy) to something we can easily measure, like the temperature of a room or a container of gas.

So when you see an equation like $E = \frac{3}{2} k T$, it means that the average energy $E$ of particles in a system is proportional to the temperature $T$ of that system, with $k$ being the proportionality constant that makes the units on both sides of the equation match up.