Thermodynamics: Gas
Terms and Formulae
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
.
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.
Einstein Condensation Temperature
-
The temperature below which Einstein Condensation significantly occurs,
given by
τ
âÉá
.
âÉá
.
Equipartition
-
A classical shortcut that assigns to one particle energy of
τ
per degree of freedom in the classical
expression of its energy.
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) =
.
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 VâÉá
.
We define the heat capacity at constant pressure to be:
C pâÉá
.
C VâÉá
.
We define the heat capacity at constant pressure to be:
C pâÉá
.
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 |
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 |
C
V =
N
C
p =
N
|
| The Fermi-Dirac 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 Bose-Einstein Distribution Function |
f (
) =
|
) = e
(μ-
log
log
+
Nτ
=
(3Π
2
n)2/3
N





