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Sackur–Tetrode Equation Using Internal Energy

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 product of internal energy and mass of a particle to the 3/2 power. It also increases logarithmically with the volume. 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 to the 5/2 power. Internal energy equals 3/2 times the product of the Boltzmann constant, particle number and the temperature.

Formula

{QuantityVariable["S", "Entropy"] == (5/2 + Log[(8*Pi^(3/2)*((Quantity[1, "PlanckConstant"^(-2)]*QuantityVariable["m", "Mass"]*QuantityVariable["U", "Energy"])/QuantityVariable["N", "Unitless"])^(3/2)*Row[{QuantityVariable["V", "Volume"]/QuantityVariable["N", "Unitless"]}])/(3*Sqrt[3])])*Quantity[1, "BoltzmannConstant"]*QuantityVariable["N", "Unitless"], QuantityVariable["U", "Energy"] == Quantity[3/2, "BoltzmannConstant"]*QuantityVariable["N", "Unitless"]*QuantityVariable["T", "Temperature"]}

symbol description physical quantity
S absolute entropy "Entropy"
m mass of a particle "Mass"
N particle number "Unitless"
U internal energy "Energy"
V volume "Volume"
T temperature "Temperature"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Sackur\[Dash]Tetrode Equation Using Internal Energy"]
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Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Sackur\[Dash]Tetrode Equation Using Internal Energy"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Sackur\[Dash]Tetrode Equation Using Internal Energy"], \ {QuantityVariable["V","Volume"] -> Quantity[1, ("Meters")^3], QuantityVariable["T","Temperature"] -> Quantity[273.15`, "Kelvins"]}]
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Source Metadata

  • Creator:
  • Date: 1912

Publisher Information