Thermodynamics is a branch of science that desribes quantitative methods for calculating equilibrium constants. We can compare the equilibrium between two species X and Y with a microscopic probability of finding those species. The macroscopic eqilibrium constant K = [Y]/[X], while the microscopic relationship is K = N_Y/N_X.

Micro vs. Macro

The Boltzmann constant k>sub>B is related to the universal gas constant R, R = k_B/N_A, where N_A is Avagradro's number. The Boltzmann constant has units of Joules/Kelvin and the gas constant has units of Joules/Mole-Kelvin. These constant have the same physical significance, but differ in the units. We could say that the Boltzmann constant is valid per molecule while the gas is valid per mole.

Boltzmann's constant

One can use the idea of microscopic levels to calculate a probability. The simplest case is a two-level system.

A two level system

Today the idea of particle populating energy levels does not seem foreign, but in 1900 this was still not a widely accepted idea. Ludwig Boltzmann derived a theory for microscopic probability. Boltzmann was ridiculed by many scientists who did not believe that there it made sense to consider energy levels. Of course, history has vindicated Boltzmann's view and his theories are the foundation of statistical mechanics and statistical thermodynamics. In order to understand the resolution of the thermal radiation problem posed in this lecture, we need one result from Boltzmann's theory.