• ### 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 n nQ.

• ### Degenerate

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

• ### 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 half-integer 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:

CVâÉá   .

We define the heat capacity at constant pressure to be:

CpâÉá   .

• ### 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 nQ =   .

• ### 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 = Nτ log   - 1 The pressure of an ideal gas is given by the ideal gas law p = The entropy of an ideal gas σ = N log   +  The energy of an ideal gas U = Nτ

 The heat capacities for an ideal gas CV = N Cp = N

 The Fermi-Dirac Distribution function f ( ) = The Fermi energy of a degenerate Fermi gas = (3Π2n)2/3

 The energy of the ground state of a Fermi gas Ugs = N The Bose-Einstein Distribution Function f ( ) = 