####
Terms

**
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**n*_{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.

**
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:

*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} = .

####
Formulas

**
The classical distribution function
** | *f* ( ) = *e*^{(μ-)/τ} = *λe*^{-/τ} |

**
The chemical potential of an ideal gas
** | |

**
The free energy of an ideal gas
** | |

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

**
The entropy of an ideal gas
** | |

**
The energy of an ideal gas
** | *U* = *Nτ* |

**
The heat capacities for an ideal gas
** | *C*_{V} = *N**C*_{p} = *N* |

**
The Fermi-Dirac Distribution function
** | *f* ( ) = |

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

**
The energy of the ground state of a Fermi gas
** | *U*_{gs} = *N* |

**
The Bose-Einstein Distribution Function
** | *f* ( ) = |