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Sackur–Tetrode Equation Using Thermal de Broglie Wavelength

The Sackur–Tetrode equation is an expression for the entropy of a monatomic classical ideal gas, which incorporates quantum considerations that give a more detailed description of its regime of validity.

The absolute entropy increases logarithmically with the volume and the reciprocal of the thermal de Broglie wavelength cubed. Higher values of the particle number also increase absolute entropy at the rate of the particle number times the logarithm of the reciprocal of the particle number. The thermal de Broglie wavelength is proportional to the reciprocal of the square root of the mass times the temperature.

Formula

{QuantityVariable["S", "Entropy"] == (5/2 + Log[QuantityVariable["V", "Volume"]/(QuantityVariable["N", "Unitless"]*QuantityVariable["Λ", "Wavelength"]^3)])*Quantity[1, "BoltzmannConstant"]*QuantityVariable["N", "Unitless"], QuantityVariable["Λ", "Wavelength"] == Quantity[1/Sqrt[2*Pi], "PlanckConstant"]/Sqrt[Quantity[1, "BoltzmannConstant"]*QuantityVariable["m", "Mass"]*QuantityVariable["T", "Temperature"]]}

symbol description physical quantity
S absolute entropy "Entropy"
N particle number "Unitless"
V volume "Volume"
Λ thermal de Broglie wavelength "Wavelength"
m mass of a particle "Mass"
T temperature "Temperature"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Sackur\[Dash]Tetrode Equation Using Thermal de \ Broglie Wavelength"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Sackur\[Dash]Tetrode Equation Using Thermal de Broglie \ Wavelength"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Sackur\[Dash]Tetrode Equation Using Thermal de Broglie \ Wavelength"], {QuantityVariable["m","Mass"] -> Quantity[1, "AtomicMassUnit"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1912

Publisher Information