Bose–Einstein Condensation Temperature for Noninteracting Bosons Using Number Density

The Bose–Einstein condensation temperature is the temperature at which a free Bose gas transitions to a Bose–Einstein condensate. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point macroscopic quantum phenomena become apparent.

The Bose-Einstein condensation temperature increases as the square of the cubic root of the boson number density increases, and increases inversely with the mass of each boson.

Formula

QuantityVariable[Subscript["T", "c"], "Temperature"] == (Quantity[(2*Pi)/Zeta[3/2]^(2/3), "ReducedPlanckConstant"^2/"BoltzmannConstant"]*(QuantityVariable["n", "InverseVolume"]/(1 + 2*QuantityVariable["s", "Unitless"]))^(2/3))/QuantityVariable["m", "Mass"]

symbol	description	physical quantity
T_c	Bose condensation temperature	"Temperature"
m	mass	"Mass"
n	boson number density	"InverseVolume"
s	particle spin	"Unitless"

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Get the resource:

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$ResourceObject["Bose\[Dash]Einstein Condensation Temperature for \ Noninteracting Bosons Using Number Density"]$

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Get the formula:

In[2]:=

$FormulaData[ ResourceObject[ "Bose\[Dash]Einstein Condensation Temperature for Noninteracting \ Bosons Using Number Density"]]$

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Use some values:

In[3]:=

$FormulaData[ ResourceObject[ "Bose\[Dash]Einstein Condensation Temperature for Noninteracting \ Bosons Using Number Density"], {QuantityVariable[ "n","InverseVolume"] -> Quantity[1.5`*^10, 1/("Micrometers")^3], QuantityVariable["s","Unitless"] -> 0}]$

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Bose–Einstein Condensation Temperature for Noninteracting Bosons Using Number Density

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