The Boltzmann constant (k or k₈) is a fundamental physical constant that connects the average kinetic energy of particles in a system to its temperature. It provides the scale that links the microscopic world of atoms and molecules to the macroscopic concept of temperature.
In essence, the Boltzmann constant sets the amount of energy per degree of freedom that corresponds to one kelvin of temperature.
Key Role:
- The average kinetic energy of a single particle in an ideal gas is proportional to (1/2) kT per degree of freedom, where T is the absolute temperature.
- It appears in important relations like the ideal gas law in microscopic form: PV=NkTPV = NkT, where NN is number of particles.
- It serves as a bridge between thermodynamics and statistical mechanics.
Value:
Approximately 1.38×10−231.38 \times 10^{-23} joules per kelvin (J/K).
Examples:
- Explains why increasing temperature increases particle motion.
- Central to formulas for entropy, distribution functions, and thermal noise.
- Used in defining the Kelvin temperature scale based on fundamental constants.
The Boltzmann constant is a cornerstone of physics that helps translate thermal energy concepts from the atomic scale to everyday temperatures.