
Bose Gas
A Bose gas is a gas consisting of bosons.

Boson
A boson is a particle with integer spin.

Classical Regime
The classical regime is that in which gases behave classically, namely without demonstrating bosonic or fermionic character. We can define the regime as f 1 or nn_{Q}.

Degenerate
Term used for a gas when it is too dense to be considered as being in the classical regime, i.e. n > n_{Q}.

Distribution Function
The distribution function, f, gives the average number of particles in an orbital.

Einstein Condensation
Also known as bose condensation, the effect of boson crowding in the ground orbital.

Einstein Condensation Temperature
The temperature below which Einstein Condensation significantly occurs, given by τ_{}âÉá.

Equipartition
A classical shortcut that assigns to one particle energy of τ per degree of freedom in the classical expression of its energy.

Fermi Energy
The Fermi energy is defined as the chemical potential at a temperature of zero: μ(τ = 0) = .

Fermi Gas
A Fermi gas is a gas consisting of fermions.

Fermion
A fermion is a particle with halfinteger spin.

Heat Capacity
The heat capacity of a gas is a measure of how much heat the gas can hold. We define the heat capacity at constant volume to be:
C_{V}âÉá.
We define the heat capacity at constant pressure to be:
C_{p}âÉá. 
Ideal Gas
A gas of particles that do not interact with each other and are in the classical regime.

Quantum Concentration
The quantum concentration marks the concentration transition between the classical and quantum regimes, and is defined as n_{Q} = .
Terms
Formulas
The classical distribution function 
f () = e^{(μ)/τ} = λe^{/τ}

The chemical potential of an ideal gas 
μ = τ log

The free energy of an ideal gas 
F = Nτlog  1

The pressure of an ideal gas is given by the ideal gas law 
p =

The entropy of an ideal gas 
σ = Nlog +

The energy of an ideal gas 
U = Nτ

The heat capacities for an ideal gas 
C_{V} = N
C_{p} = N

The FermiDirac Distribution function 
f () =

The Fermi energy of a degenerate Fermi gas 
= (3Π^{2}n)^{2/3}

The energy of the ground state of a Fermi gas 
U_{gs} = N

The BoseEinstein Distribution Function 
f () =
