In
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
, the excitation temperature () is defined for a population of
particles
In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass.
They vary greatly in size or quantity, from s ...
via the
Boltzmann factor. It satisfies
:
where
* is the number of particles in an upper (''e.g.'' excited)
state
State most commonly refers to:
* State (polity), a centralized political organization that regulates law and society within a territory
**Sovereign state, a sovereign polity in international law, commonly referred to as a country
**Nation state, a ...
;
* is the
statistical weight
In statistical mechanics, multiplicity (also called statistical weight) refers to the number of microstate (statistical mechanics), microstates corresponding to a particular macrostate of a thermodynamic system. Commonly denoted \Omega, it is rela ...
of those upper-state particles;
* is the number of particles in a lower (''e.g.''
ground) state;
* is the statistical weight of those lower-state particles;
* is the
exponential function;
* is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the ...
;
* is the difference in energy between the upper and lower states.
Thus the excitation temperature is the temperature at which we would expect to find a system with this ratio of level populations. However it has no actual physical meaning except when in local
thermodynamic equilibrium
Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
. The excitation temperature can even be negative for a system with inverted levels (such as a
maser).
In observations of the
21 cm line of
hydrogen
Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
, the apparent value of the excitation temperature is often called the "spin temperature".
References
Temperature
{{thermodynamics-stub