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Bose Gas
A Bose gas is a gas consisting of bosons.
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Boson
A boson is a particle with integer spin.
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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.
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Degenerate
Term used for a gas when it is too dense to be considered as being in the classical regime, i.e. n > nQ.
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Distribution Function
The distribution function, f, gives the average number of particles in an orbital.
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Einstein Condensation
Also known as bose condensation, the effect of boson crowding in the ground orbital.
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Einstein Condensation Temperature
The temperature below which Einstein Condensation significantly occurs, given by τ
âÉá
.
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Equipartition
A classical shortcut that assigns to one particle energy of
τ per degree of freedom in the classical expression of its energy.
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Fermi Energy
The Fermi energy
is defined as the chemical potential at a temperature of zero: μ(τ = 0) =
.
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Fermi Gas
A Fermi gas is a gas consisting of fermions.
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Fermion
A fermion is a particle with half-integer spin.
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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.
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Ideal Gas
A gas of particles that do not interact with each other and are in the classical regime.
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Quantum Concentration
The quantum concentration marks the concentration transition between the classical and quantum regimes, and is defined as nQ =
.
Terms
Formulas
The classical distribution function |
f (
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The chemical potential of an ideal gas |
μ = τ log
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The free energy of an ideal gas |
F = Nτ
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The pressure of an ideal gas is given by the ideal gas law |
p =
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The entropy of an ideal gas |
σ = N
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The energy of an ideal gas |
U =
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The heat capacities for an ideal gas |
CV =
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Cp =
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The Fermi-Dirac Distribution function |
f (
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The Fermi energy of a degenerate Fermi gas |
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The energy of the ground state of a Fermi gas |
Ugs =
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The Bose-Einstein Distribution Function |
f (
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