Terms and Formulae
Terms
Bose Gas
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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.
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:
CVâɡ


.
We define the heat capacity at constant pressure to be:
Cpâɡ


.
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
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The classical distribution function
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The chemical potential of an ideal gas
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The free energy of an ideal gas
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The pressure of an ideal gas is given by the ideal gas law
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p =
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The entropy of an ideal gas
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The energy of an ideal gas
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U = Nτ
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The heat capacities for an ideal gas
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CV = N
Cp = N
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The Fermi-Dirac Distribution function
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f (  ) =
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The Fermi energy of a degenerate Fermi gas
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 =  (3 Π2n) 2/3
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The energy of the ground state of a Fermi gas
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Ugs = N
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The Bose-Einstein Distribution Function
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f (  ) =
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