Bose–Einstein Condensation Temperature for Noninteracting Bosons Using Volume

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 ratio between particle number and volume 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", "Unitless"]/((1 + 2*QuantityVariable["s", "Unitless"])*QuantityVariable["V", "Volume"]))^(2/3))/QuantityVariable["m", "Mass"]

symbol	description	physical quantity
T_c	Bose condensation temperature	"Temperature"
m	mass	"Mass"
N	particle number	"Unitless"
s	particle spin	"Unitless"
V	volume	"Volume"

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Get the resource:

In[1]:=

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

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Get the formula:

In[2]:=

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

Out[2]=

Use some values:

In[3]:=

$FormulaData[ ResourceObject[ "Bose\[Dash]Einstein Condensation Temperature for Noninteracting \ Bosons Using Volume"], {QuantityVariable["V","Volume"] -> Quantity[0.001`, ("Micrometers")^3]}]$

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Bose–Einstein Condensation Temperature for Noninteracting Bosons Using Volume

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