It can be modified to deal with quantum systems consisting of particles with either integer or half integer spins, resulting in the Bose-Einstein and Fermi-Dirac statistical distributions.
This equation can be derived through the ergodic hypothesis coupled with application of Stirling's approximation to the partition function, and contains a term in its denominator for temperature normalization. It can be modified to deal with quantum systems consisting of particles with either integer or half integer spins, resulting in the Bose-Einstein and Fermi-Dirac statistical distributions. It utilizes a namesake constant that is equal to the ratio of the gas constant and Avagadro's number and it gives an inverse exponential relationship between the probability of occupying an energy state and the total system energy. For 10 points, name this statistical distribution of energy between identical, distinguishable particles in an ideal gas named for a Scottish and Austrian physicist.
This equation can be derived through the ergodic hypothesis coupled with application of Stirling's approximation to the partition function, and contains a term in its denominator for temperature normalization.
{Maxwell-Boltzmann} distribution [prompt on {Boltzmann distribution}]