The value of the Boltzmann constant (k) is not directly derived from fundamental constants like the proton mass or electron charge. Instead, its value is determined empirically through experimental measurements. The Boltzmann constant relates the average kinetic energy of particles in a gas to the temperature of the system and is a fundamental constant in statistical mechanics.
The Boltzmann constant is defined as the gas constant (R) divided by Avogadro's number (Nₐ):
k = R / Nₐ
The gas constant R can be measured experimentally, and Avogadro's number Nₐ is determined based on the definition of the mole, which is a fundamental quantity in chemistry.
The value of the Boltzmann constant has been determined through various experimental techniques, including measurements of the behavior of gases, the specific heat capacities of substances, and the study of blackbody radiation. These experiments involve statistical analyses and thermodynamic principles to establish the relationship between temperature, energy, and entropy.
The Boltzmann constant is not directly related to the mass of particles or the properties of spacetime as described by Einstein's theory of relativity. However, it is an essential constant that allows us to connect the microscopic behavior of particles to macroscopic phenomena, such as temperature and thermodynamic properties of materials.
It's important to note that the Boltzmann constant is deeply connected to the foundations of statistical mechanics and thermodynamics, which provide a framework for understanding the behavior of large ensembles of particles and their statistical properties.