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Bose–Einstein Condensation Temperature for Noninteracting Bosons Using Pressure

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 pressure 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"]*((Quantity[1, "BoltzmannConstant"^(-1)]*QuantityVariable["P", "Pressure"])/((1 + 2*QuantityVariable["s", "Unitless"])*QuantityVariable[Subscript["T", "c"], "Temperature"]))^(2/3))/QuantityVariable["m", "Mass"]

symbol description physical quantity
Tc Bose condensation temperature "Temperature"
m mass "Mass"
P pressure "Pressure"
s particle spin "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Bose\[Dash]Einstein Condensation Temperature for \ Noninteracting Bosons Using Pressure"]
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Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Bose\[Dash]Einstein Condensation Temperature for Noninteracting \ Bosons Using Pressure"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Bose\[Dash]Einstein Condensation Temperature for Noninteracting \ Bosons Using Pressure"], {QuantityVariable[ \!\(\*SubscriptBox[\("T"\), \("c"\)]\),"Temperature"] -> None, QuantityVariable["P","Pressure"] -> Quantity[0.0497`, "Atmospheres"], QuantityVariable["m","Mass"] -> Quantity[4, "AtomicMassUnit"]}]
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Source Metadata

  • Creator:
  • Date: 1925

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