For systems with many molecules at equilibrium at temperature, frequency distributions {Boltzmann distribution, statistics}| can plot frequency against molecule energy. y(E) = e^(- E / (k * T)), where E is molecule energy level, y(E) is frequency for molecule energy level, e is natural-logarithm base, k is Boltzmann constant, and T is absolute temperature.
energy
Particle-energy probability is partition number and is relative frequency of that energy in Boltzmann distribution. Most-probable energies are near average energy. Total energy is integral of Boltzmann distribution.
comparison
At temperatures above 50 K, Boltzmann distributions look like Gaussian distributions.
equilibrium
Systems at equilibrium have Boltzmann distribution, because that distribution has much higher probability than other distributions with same total energy. Boltzmann distribution has the most combinations that can give total energy.
equilibrium: entropy
For that reason, Boltzmann distribution has lowest probability of molecule being in any one energy level, so Boltzmann distribution has the most entropy and least order. Entropy S equals Boltzmann constant k times combination-number C natural logarithm: S = k * ln(C).
Physical Sciences>Physics>Heat>Statistical Mechanics
5-Physics-Heat-Statistical Mechanics
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0224