Astrophysics (index) | about |

Ludwig Eduard Boltzmann is responsible for a lot of equations
and in various fields, different equations are termed the
**Boltzmann Equation**.

In the field of Stellar Structure, an equation giving
the count of atoms at different possible Atomic Excitation
levels is given the name, or sometimes
**Boltzmann Relation** (which is also ambiguous). One form:

N^{i+1}g^{i+1}———— = ———— e^{-(Ei+1-Ei)/kT}N^{i}g^{i}

- N
^{i+1}, N^{i}- Number Density of two States of Excitation i and i+1. - g
^{i+1}, g^{i}- Quantum-Mechanical Degeneracy Weights. - k - Boltzmann Constant.
- T - Temperature.

This equation is related to the **Boltzmann Distribution**
(frequency of Particles at various states,
*not* the same as the Maxwell-Boltzmann Distribution,
which is the distribution of (say) the Kinetic Energy
of particles in (say) a gas) incorporating
a **Boltzmann Factor** (e^{-(E1-E2)/kT})
giving the relative probability of two energy levels,
and relating the ratio of the two
terms, N_{x}/g_{x}
(the number of atoms in specific Quantum state)
to it.

Degeneracy Weight

State of Excitation

Stefan-Boltzmann Constant (σ)

Temperature