# Thermodynamics: Gas

### Contents

#### 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 nnQ.
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 τâÉá.
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 = 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 CV = NCp = 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 () =